NCERT Solutions for Class 9 Maths Chapter 7 Triangles

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# NCERT Solutions for Class 9 Maths Chapter 7 Triangles

Edited By Ramraj Saini | Updated on Sep 27, 2023 10:38 PM IST

## NCERT Solutions for Class 9 Maths Chapter 7 Triangles

NCERT solutions for class 9 maths chapter 7 Triangles are provided here. These are developed by subject matter expert at careersers360 considering latest CBSE syllabus 2023. Also these provide step by step solutions to all NCERT problems in comprehensive and simple way therefore these are easy to understand and ultimately beneficial for exams. In Class 9 Maths NCERT Syllabus Triangles, you will learn something of a higher level. NCERT triangles class 9 questions and answers can be a good tool whenever you are stuck in any of the problems. This Class 9 NCERT book chapter will be covering the properties of triangles like congruence of triangles, isosceles triangle, etc in detail.

By using NCERT class 9 maths chapter 7 question answer, you can prepare 360 degree for your school as well as for the competitive examinations. Here you will get NCERT solutions for class 9 Maths also.

## Triangles Class 9 Solutions - Important Formulae And Points

Congruence:

• Congruent refers to figures that are identical in all aspects, including their shapes and sizes. For example, two circles with the same radii or two squares with the same side lengths are considered congruent.

Congruent Triangles:

• Two triangles are considered congruent if and only if one of them can be superimposed (placed or overlaid) over the other in such a way that they entirely cover each other.

>> Congruence Rules for Triangles:

• Side-Angle-Side (SAS) Congruence:

• Angle-Side-Angle (ASA) Congruence:

• Angle-Angle-Side (AAS) Congruence:.

• Side-Side-Side (SSS) Congruence:

• Right-Angle Hypotenuse Side (RHS) Congruence:

Free download NCERT Solutions for Class 9 Maths Chapter 7 Triangles for CBSE Exam.

## Triangles Class 9 NCERT Solutions (Intext Questions and Exercise)

NCERT solutions for class 10 maths chapter 7 Triangles - Excercise: 7.1

In the given triangles we are given that:-

(i) $\small AC=AD$

(ii) Further, it is given that AB bisects angle A. Thus $\angle$ BAC $=\ \angle$ BAD.

(iii) Side AB is common in both the triangles. $AB=AB$

Hence by SAS congruence, we can say that : $\small \Delta ABC\cong \Delta ABD$

By c.p.c.t. (corresponding parts of congruent triangles are equal) we can say that $BC\ =\ BD$

It is given that :-

(ii) $\small \angle DAB= \angle CBA$

(iii) Side AB is common in both the triangles.

So, by SAS congruence, we can write :

$\small \Delta ABD\cong \Delta BAC$

In the previous part, we have proved that $\small \Delta ABD\cong \Delta BAC$ .

Thus by c.p.c.t. , we can write : $\small BD=AC$

In the first part we have proved that $\small \Delta ABD\cong \Delta BAC$ .

Thus by c.p.c.t. , we can conclude :

$\small \angle ABD= \angle BAC$

In the given figure consider $\Delta$ AOD and $\Delta$ BOC.

(ii) $\angle$ A = $\angle$ B (given that the line AB is perpendicular to AD and BC)

(iii) $\angle$ AOD = $\angle$ BOC (vertically opposite angles).

Thus by AAS Postulate, we have

$\Delta AOD\ \cong \ \Delta BOC$

Hence by c.p.c.t. we can write : $AO\ =\ OB$

And thus CD bisects AB.

In the given figure, consider $\Delta$ ABC and $\Delta$ CDA :

(i) $\angle\ BCA\ =\ \angle DAC$

(ii) $\angle\ BAC\ =\ \angle DCA$

(iii) Side AC is common in both the triangles.

Thus by ASA congruence, we have :

$\Delta ABC\ \cong \ \Delta CDA$

In the given figure consider $\small \Delta APB$ and $\small \Delta AQB$ ,

(i) $\angle P\ =\ \angle Q$ (Right angle)

(ii) $\angle BAP\ =\ \angle BAQ$ (Since it is given that I is bisector)

(iii) Side AB is common in both the triangle.

Thus AAS congruence, we can write :

$\small \Delta APB\cong \Delta AQB$

In the previous part we have proved that $\small \Delta APB\cong \Delta AQB$ .

Thus by c.p.c.t. we can write :

$BP\ =\ BQ$

Thus B is equidistant from arms of angle A.

From the given figure following result can be drawn:-

$\angle BAD\ =\ \angle EAC$

Adding $\angle DAC$ to the both sides, we get :

$\angle BAD\ +\ \angle DAC\ =\ \angle EAC\ +\ \angle DAC$

$\angle BAC\ =\ \angle EAD$

Now consider $\Delta ABC$ and $\Delta ADE$ , :-

(i) $AC\ =\ AE$ (Given)

(ii) $\angle BAC\ =\ \angle EAD$ (proved above)

(iii) $AB\ =\ AD$ (Given)

Thus by SAS congruence we can say that :

$\Delta ABC\ \cong \ \Delta ADE$

Hence by c.p.c.t., we can say that : $BC\ =\ DE$

From the figure, it is clear that :
$\angle EPA\ =\ \angle DPB$

Adding $\angle DPE$ both sides, we get :

$\angle EPA\ +\ \angle DPE =\ \angle DPB\ +\ \angle DPE$

or $\angle DPA =\ \angle EPB$

Now, consider $\Delta DAP$ and $\Delta EBP$ :

(i) $\angle DPA =\ \angle EPB$ (Proved above)

(ii) $AP\ =\ BP$ (Since P is the midpoint of line AB)

(iii) $\small \angle BAD=\angle ABE$ (Given)

Hence by ASA congruence, we can say that :

$\small \Delta DAP\cong \Delta EBP$

In the previous part we have proved that $\small \Delta DAP\cong \Delta EBP$ .

Thus by c.p.c.t., we can say that :

$\small AD=BE$

Consider $\Delta AMC$ and $\Delta BMD$ ,

(i) $AM\ =\ BM$ (Since M is the mid-point)

(ii) $\angle CMA\ =\ \angle DMB$ (Vertically opposite angles are equal)

(iii) $CM\ =\ DM$ (Given)

Thus by SAS congruency, we can conclude that :

$\small \Delta AMC\cong \Delta BMD$

In the previous part, we have proved that $\small \Delta AMC\cong \Delta BMD$ .

By c.p.c.t. we can say that : $\angle ACM\ =\ \angle BDM$

This implies side AC is parallel to BD.

Thus we can write : $\angle ACB\ +\ \angle DBC\ =\ 180^{\circ}$ (Co-interior angles)

and, $90^{\circ}\ +\ \angle DBC\ =\ 180^{\circ}$

or $\angle DBC\ =\ 90^{\circ}$

Hence $\small \angle DBC$ is a right angle.

Consider $\Delta DBC$ and $\Delta ACB$ ,

(i) $BC\ =\ BC$ (Common in both the triangles)

(ii) $\angle ACB\ =\ \angle DBC$ (Right angle)

(iii) $DB\ =\ AC$ (By c.p.c.t. from the part (a) of the question.)

Thus SAS congruence we can conclude that :

$\small \Delta DBC\cong \Delta ACB$

In the previous part we have proved that $\Delta DBC\ \cong \ \Delta ACB$ .

Thus by c.p.c.t., we can write : $DC\ =\ AB$

$DM\ +\ CM\ =\ AM\ +\ BM$

or $CM\ +\ CM\ =\ AB$ (Since M is midpoint.)

or $\small CM=\frac{1}{2}AB$ .

Hence proved.

NCERT Class 9 Maths Chapter 7 Question Answer - Excercise: 7.2

In the triangle ABC,

Since AB = AC, thus $\angle B\ =\ \angle C$

or $\frac{1}{2}\angle B\ =\ \frac{1}{2}\angle C$

or $\angle OBC\ =\ \angle OCB$ (Angles bisectors are equal)

Thus $\small OB=OC$ as sides opposite to equal are angles are also equal.

Consider $\Delta AOB$ and $\Delta AOC$ ,

(i) $AB\ =\ AC$ (Given)

(ii) $AO\ =\ AO$ (Common in both the triangles)

(iii) $OB\ =\ OC$ (Proved in previous part)

Thus by SSS congruence rule, we can conclude that :

$\Delta AOB\ \cong \ \Delta AOC$

Now, by c.p.c.t.,

$\angle BAO\ =\ \angle CAO$

Hence AO bisects $\angle A$ .

Consider $\Delta$ ABD and $\Delta$ ADC,

(i) $AD\ =\ AD$ (Common in both the triangles)

(ii) $\angle ADB\ =\ \angle ADC$ (Right angle)

(iii) $BD\ =\ CD$ (Since AD is the bisector of BC)

Thus by SAS congruence axiom, we can state :

$\Delta ADB\ \cong \ \Delta ADC$

Hence by c.p.c.t., we can say that : $\small AB=AC$

Thus $\Delta ABC$ is an isosceles triangle with AB and AC as equal sides.

Consider $\Delta AEB$ and $\Delta AFC$ ,

(i) $\angle A$ is common in both the triangles.

(ii) $\angle AEB\ =\ \angle AFC$ (Right angles)

(iii) $AB\ =\ AC$ (Given)

Thus by AAS congruence axiom, we can conclude that :

$\Delta AEB\ \cong \Delta AFC$

Now, by c.p.c.t. we can say : $BE\ =\ CF$

Hence these altitudes are equal.

Consider $\Delta ABE$ and $\Delta ACF$ ,

(i) $\angle A$ is common in both the triangles.

(ii) $\angle AEB\ =\ \angle AFC$ (Right angles)

(iii) $BE\ =\ CF$ (Given)

Thus by AAS congruence, we can say that :

$\small \Delta ABE \cong \Delta ACF$

From the prevoius part of the question we found out that : $\Delta ABE\ \cong \Delta ACF$

Now, by c.p.c.t. we can say that : $AB\ =\ AC$

Hence $\Delta \ ABC$ is an isosceles triangle.

Consider $\Delta ABD$ and $\Delta ACD$ ,

(i) $AD\ =\ AD$ (Common in both the triangles)

(ii) $AB\ =\ AC$ (Sides of isosceles triangle)

(iii) $BD\ =\ CD$ (Sides of isosceles triangle)

Thus by SSS congruency, we can conclude that :

$\small \angle ABD\ \cong \ \angle ACD$

Consider $\Delta$ ABC,
It is given that AB = AC

So, $\angle ACB = \angle ABC$ (Since angles opposite to the equal sides are equal.)

Similarly in $\Delta$ ACD,

and $\angle ADC = \angle ACD$
So,

$\angle CAB + \angle ACB + \angle ABC = 180^{\circ}$

$\angle CAB\ +\ 2\angle ACB = 180^{\circ}$
or $\angle CAB\ = 180^{\circ}\ -\ 2\angle ACB$ ...........................(i)

And in $\Delta$ ADC,
$\angle CAD\ = 180^{\circ}\ -\ 2\angle ACD$ ..............................(ii)

Adding (i) and (ii), we get :
$\angle CAB\ +\ \angle CAD\ = 360^{\circ}\ -\ 2\angle ACD\ -\ 2\angle ACB$

or $180^{\circ}\ = 360^{\circ}\ -\ 2\angle ACD\ -\ 2\angle ACB$

and $\angle BCD\ =\ 90^{\circ}$

In the triangle ABC, sides AB and AC are equal.

We know that angles opposite to equal sides are also equal.

Thus, $\angle B\ =\ \angle C$

Also, the sum of the interior angles of a triangle is $180^{\circ}$ .

So, we have :

$\angle A\ +\ \angle B\ +\ \angle C\ =\ 180^{\circ}$

or $90^{\circ} +\ 2\angle B\ =\ 180^{\circ}$

or $\angle B\ =\ 45^{\circ}$

Hence $\angle B\ =\ \angle C\ =\ 45^{\circ}$

Consider a triangle ABC which has all sides equal.

We know that angles opposite to equal sides are equal.

Thus we can write : $\angle A\ =\ \angle B\ =\ \angle C$

Also, the sum of the interior angles of a triangle is $180 ^{\circ}$ .

Hence, $\angle A\ +\ \angle B\ +\ \angle C\ =\ 180^{\circ}$

or $3\angle A\ =\ 180^{\circ}$

or $\angle A\ =\ 60^{\circ}$

So, all the angles of the equilateral triangle are equal ( $60^{\circ}$ ).

Class 9 Triangles NCERT Solutions - Excercise: 7.3

Consider $\Delta ABD$ and $\Delta ACD$ ,

(i) $AD\ =\ AD$ (Common)

(ii) $AB\ =\ AC$ (Isosceles triangle)

(iii) $BD\ =\ CD$ (Isosceles triangle)

Thus by SSS congruency we can conclude that :

$\small \Delta ABD\cong \Delta ACD$

Consider $\Delta ABP$ and $\Delta ACP$ ,

(i) $AP$ is common side in both the triangles.

(ii) $\angle PAB\ =\ \angle PAC$ (This is obtained from the c.p.c.t. as proved in the previous part.)

(iii) $AB\ =\ AC$ (Isosceles triangles)

Thus by SAS axiom, we can conclude that :

$\small \Delta ABP \cong \Delta ACP$

In the first part, we have proved that $\small \Delta ABD\cong \Delta ACD$ .

So, by c.p.c.t. $\angle PAB\ =\ \angle PAC$ .

Hence AP bisects $\angle A$ .

Now consider $\Delta BPD$ and $\Delta CPD$ ,

(i) $PD\ =\ PD$ (Common)

(ii) $BD\ =\ CD$ (Isosceles triangle)

(iii) $BP\ =\ CP$ (by c.p.c.t. from the part (b))

Thus by SSS congruency we have :

$\Delta BPD\ \cong \ \Delta CPD$

Hence by c.p.c.t. we have : $\angle BDP\ =\ \angle CDP$

or AP bisects $\angle D$ .

In the previous part we have proved that $\Delta BPD\ \cong \ \Delta CPD$ .

Thus by c.p.c.t. we can say that : $\angle BPD\ =\ \angle CPD$

Also, $BP\ =\ CP$

SInce BC is a straight line, thus : $\angle BPD\ +\ \angle CPD\ =\ 180^{\circ}$

or $2\angle BPD\ =\ 180^{\circ}$

or $\angle BPD\ =\ 90^{\circ}$

Hence it is clear that AP is a perpendicular bisector of line BC.

Consider $\Delta ABD$ and $\Delta ACD$ ,

(i) $AB\ =\ AC$ (Given)

(ii) $AD\ =\ AD$ (Common in both triangles)

(iii) $\angle ADB\ =\ \angle ADC\ =\ 90^{\circ}$

Thus by RHS axiom we can conclude that :

$\Delta ABD\ \cong \ \Delta ACD$

Hence by c.p.c.t. we can say that : $BD\ =\ CD$ or AD bisects BC.

In the previous part of the question we have proved that $\Delta ABD\ \cong \ \Delta ACD$

Thus by c.p.c.t., we can write :

$\angle BAD\ =\ \angle CAD$

Hence $AD$ bisects $\angle A$ .

(i) $\small \Delta ABM \cong \Delta PQN$

(ii) $\small \Delta ABC \cong \Delta PQR$

(i) From the figure we can say that :

$BC\ =\ QR$

or $\frac{1}{2}BC\ =\ \frac{1}{2}QR$

or $BM\ =\ QN$

Now, consider $\Delta ABM$ and $\Delta PQN$ ,

(a) $AM\ =\ PN$ (Given)

(b) $AB\ =\ PQ$ (Given)

(c) $BM\ =\ QN$ (Prove above)

Thus by SSS congruence rule, we can conclude that :

$\small \Delta ABM \cong \Delta PQN$

(ii) Consider $\Delta ABC$ and $\Delta PQR$ :

(a) $AB\ =\ PQ$ (Given)

(b) $\angle ABC\ =\ \angle PQR$ (by c.p.c.t. from the above proof)

(c) $BC\ =\ QR$ (Given)

Thus by SAS congruence rule,

$\small \Delta ABC \cong \Delta PQR$

Using the given conditions, consider $\Delta BEC$ and $\Delta CFB$ ,

(i) $\angle BEC\ =\ \angle CFB$ (Right angle)

(ii) $BC\ =\ BC$ (Common in both the triangles)

(iii) $BE\ =\ CF$ (Given that altitudes are of the same length. )

Thus by RHS axiom, we can say that : $\Delta BEC\ \cong \Delta CFB$

Hence by c.p.c.t., $\angle B\ =\ \angle C$

And thus $AB\ =\ AC$ (sides opposite to equal angles are also equal). Thus ABC is an isosceles triangle.

Consider $\Delta ABP$ and $\Delta ACP$ ,

(i) $\angle APB\ =\ \angle APC\ =\ 90^{\circ}$ (Since it is given that AP is altitude.)

(ii) $AB\ =\ AC$ (Isosceles triangle)

(iii) $AP\ =\ AP$ (Common in both triangles)

Thus by RHS axiom we can conclude that :

$\Delta ABP\ \cong \Delta ACP$

Now, by c.p.c.t.we can say that :

$\angle B\ =\ \angle C$

Class 9 maths chapter 7 NCERT solutions - Excercise: 7.4

Consider a right-angled triangle ABC with right angle at A.

We know that the sum of the interior angles of a triangle is 180.

So, $\angle A\ +\ \angle B\ +\ \angle C\ =\ 180^{\circ}$

or $90^{\circ}\ +\ \angle B\ +\ \angle C\ =\ 180^{\circ}$

or $\angle B\ +\ \angle C\ =\ 90^{\circ}$

Hence $\angle B$ and $\angle C$ are less than $\angle A$ ( $90^{\circ}$ ).

Also, the side opposite to the largest angle is also the largest.

Hence the side BC is largest is the hypotenuse of the $\Delta ABC$ .

Hence it is proved that in a right-angled triangle, the hypotenuse is the longest side.

We are given that,

$\small \angle PBC < \angle QCB$ ......................(i)

Also, $\angle ABC\ +\ \angle PBC\ =\ 180^{\circ}$ (Linear pair of angles) .....................(ii)

and $\angle ACB\ +\ \angle QCB\ =\ 180^{\circ}$ (Linear pair of angles) .....................(iii)

From (i), (ii) and (iii) we can say that :

$\angle ABC\ > \ \angle ACB$

Thus $AC\ > AB$ ( Sides opposite to the larger angle is larger.)

In this question, we will use the property that sides opposite to larger angle are larger.

We are given $\small \angle B <\angle A$ and $\small \angle C <\angle D$ .

Thus, $BO\ > AO$ ..............(i)

and $OC\ > OD$ ...............(ii)

Adding (i) and (ii), we get :

$AO\ +\ OD\ <\ BO\ +\ OC$

or $AD\ <\ BC$

Hence proved.

Consider $\Delta ADC$ in the above figure :

$AD\ <\ CD$ (Given)

Thus $\angle CAD\ > \angle ACD$ (as angle opposite to smaller side is smaller)

Now consider $\Delta ABC$ ,

We have : $BC\ > AB$

and $\angle BAC\ > \angle ACB$

Adding the above result we get,

$\angle BAC\ +\ \angle CAD > \angle ACB\ +\ \angle ACD$

or $\small \angle A>\angle C$

Similarly, consider $\Delta ABD$ ,

we have $AB\ <\ AD$

Therefore $\angle ABD\ > \angle ADB$

and in $\Delta BDC$ we have,

$CD\ >\ BC$

and $\angle CBD\ >\ \angle CDB$

from the above result we have,

$\angle ABD\ +\ \angle CBD\ >\ \angle ADB\ +\ \angle CDB$

or $\small \angle B>\angle D$

Hence proved.

We are given that $\small PR>PQ$ .

Thus $\angle PQR\ =\ \angle PRQ$

Also, PS bisects $\small \angle QPR$ , thus :

$\angle QPS\ =\ \angle RPS$

Now, consider $\Delta QPS$ ,

$\angle PSR\ =\ \angle PQR\ +\ \angle QPS$ (Exterior angle)

Now, consider $\Delta PSR$ ,

$\angle PSQ\ =\ \angle PRQ\ +\ \angle RPS$

Thus from the above the result we can conclude that :

$\small \angle PSR>\angle PSQ$

Consider a right-angled triangle ABC with right angle at B.

Then $\angle B\ >\ \angle A\ or\ \angle C$ (Since $\angle B\ =\ 90^{\circ}$ )

Thus the side opposite to largest angle is also largest. $AC\ >\ BC\ or\ AB$

Hence the given statement is proved that all line segments are drawn from a given point, not on it, the perpendicular line segment is the shortest.

Triangles class 9 NCERT solutions - Excercise: 7.5

We know that circumcenter of a triangle is equidistant from all the vertices. Also, circumcenter is the point of intersection of the perpendicular bisectors of the sides of a triangle.

Thus, draw perpendicular bisectors of each side of the triangle ABC. And let them meet at a point, say O.

Hence O is the required point which is equidistant from all the vertices.

The required point is called in-centre of the triangle. This point is the intersection of the angle bisectors of the interior angles of a triangle.

Hence the point can be found out in this case just by drawing angle bisectors of all the angles of the triangle.

A : where there are different slides and swings for children,

B : near which a man-made lake is situated,

C : which is near to a large parking and exit.

Where should an icecream parlour be set up so that maximum number of persons can approach it? ( Hint : The parlour should be equidistant from A, B and C)

The three main points form a triangle ABC. Now we have to find a point which is equidistant from all the three points.

Thus we need to find the circumcenter of the $\Delta ABC$ .

We know that circumcenter is defined as the point as the intersection point of the perpendicular bisectors of the sides of the triangle.

Hence the required point can be found out by drawing perpendicular bisectors of $\Delta ABC$ .

For finding the number of triangles we need to find the area of the figure.

Consider the hexagonal structure :

Area of hexagon = 6 $\times$ Area of 1 equilateral

Thus area of the equilateral triangle :

$=\ \frac{\sqrt{3}}{4}\times a^2$

or $=\ \frac{\sqrt{3}}{4}\times 5^2$

or $=\ \frac{25\sqrt{3}}{4}\ cm^2$

So, the area of the hexagon is :

$=\6\times \frac{25\sqrt{3}}{4}\ =\ \frac{75\sqrt{3}}{2}\ cm^2$

And the area of an equilateral triangle having 1cm as its side is :

$=\ \frac{\sqrt{3}}{4}\times 1^2$

or $=\ \frac{\sqrt{3}}{4}\ cm^2$

Hence a number of equilateral triangles that can be filled in hexagon are :

$=\ \frac{\frac{75\sqrt{3}}{2}}{\frac{\sqrt{3}}{4}}\ =\ 150$

Similarly for star-shaped rangoli :

Area :

$=\12\times \frac{\sqrt{3}}{4}\times 5^2 \ =\ 75\sqrt{3}\ cm^2$

Thus the number of equilateral triangles are :

$=\ \frac{75\sqrt{3}}{\frac{\sqrt{3}}{4}}\ =\ 300$

Hence star-shaped rangoli has more equilateral triangles.

### NCERT Triangles Class 9 Chapter 7 - Topics

• Congruence of Triangles
• Criteria for Congruence of Triangles
• Some Properties of a Triangle
• Some More Criteria for Congruence of Triangles
• Inequalities in a Triangle

### More About NCERT Solutions For Class 9 Maths Chapter 7 Triangles

In ch 7 maths class 9, there are a total of 5 exercises with 31 questions in them. NCERT solutions for class 9 maths chapter 7 Triangles is covering the entire chapter including the optional exercises. The chapter is full of properties and theorems that's why the examples and theorems are as important as the practice exercises. There is another aspect to look at the importance of this chapter, apart from school exams this is an essential part of competitive examinations like- CAT, SSC, NTSE, INO, etc.

Also practice class 9 maths ch 7 question answer using the exercise given below.

## NCERT Solutions For Class 9 - Chapter Wise

 Chapter No. Chapter Name Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Triangles Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15

• ## NCERT Solutions for Class 9 Maths

How To Use NCERT Solutions For Class 9 Maths Chapter 7 Triangles

• Learn some basic properties of triangles using some books of previous classes.
• Go through all the theorems and examples given in the chapter.
• Once you have memorized all the theorems and properties, then you can practice the questions from practice exercises
• During the practice, you can use NCERT solutions for class 9 maths chapter 7 triangles as a helpmate.
• After doing all the exercises you can do some questions from past papers.

## NCERT Books and NCERT Syllabus

Keep Working Hard and Happy Learning!

1. What are the important topics in chapter 7 maths class 9 ?

Congruence of triangles, Criteria for congruence of triangles, Properties of triangles, Inequalities of triangles are the important topics covered in this chapter. Students can practice NCERT solutions for class 9 maths to get command in these concepts that ultimately help during the exams.

2. In NCERT Solutions for class 9 chapter 7 maths, what does the concept of "congruence of triangles" signify?

NCERT Solutions for maths chapter 7 class 9 explain that "congruence of triangles" refers to the condition where two triangles are identical copies of each other and overlap perfectly when superimposed. In simpler terms, two triangles are considered congruent when the angles and sides of one triangle are equivalent to the corresponding angles and sides of the other triangle.

3. Where can I find the complete triangles class 9 solutions ?

Here you will get the detailed NCERT solutions for class 9 maths  by clicking on the link. you can practice these solutions to command the concepts.

4. In what ways can NCERT Solutions for Class 9 Maths Chapter 7 assist in preparing for CBSE exams?

NCERT Solutions for Class 9 Maths Chapter 7 can assist students in achieving a high score and excelling in the subject in their CBSE exams. These solutions are designed based on the latest CBSE syllabus and cover all the essential topics in the respective subject. By practicing these solutions, students can gain confidence and be better prepared to face the board exams. The topics covered in these solutions are fundamental and contribute significantly to obtaining top scores. Moreover, solving problems of varying difficulty levels helps students get accustomed to answering questions of all types. Thus, these solutions are highly recommended for students as a reference and for practice in preparation for their CBSE exams.

5. How many chapters are there in the CBSE class 9 maths ?

There are 15 chapters starting from the number system to probability in the CBSE class 9 maths.

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 Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9
##### Bio Medical Engineer

The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.

4 Jobs Available

Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.

4 Jobs Available
##### Cartographer

How fascinating it is to represent the whole world on just a piece of paper or a sphere. With the help of maps, we are able to represent the real world on a much smaller scale. Individuals who opt for a career as a cartographer are those who make maps. But, cartography is not just limited to maps, it is about a mixture of art, science, and technology. As a cartographer, not only you will create maps but use various geodetic surveys and remote sensing systems to measure, analyse, and create different maps for political, cultural or educational purposes.

3 Jobs Available
##### Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

3 Jobs Available
##### GIS Expert

GIS officer work on various GIS software to conduct a study and gather spatial and non-spatial information. GIS experts update the GIS data and maintain it. The databases include aerial or satellite imagery, latitudinal and longitudinal coordinates, and manually digitized images of maps. In a career as GIS expert, one is responsible for creating online and mobile maps.

3 Jobs Available
##### Ethical Hacker

A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.

3 Jobs Available
##### Database Architect

If you are intrigued by the programming world and are interested in developing communications networks then a career as database architect may be a good option for you. Data architect roles and responsibilities include building design models for data communication networks. Wide Area Networks (WANs), local area networks (LANs), and intranets are included in the database networks. It is expected that database architects will have in-depth knowledge of a company's business to develop a network to fulfil the requirements of the organisation. Stay tuned as we look at the larger picture and give you more information on what is db architecture, why you should pursue database architecture, what to expect from such a degree and what your job opportunities will be after graduation. Here, we will be discussing how to become a data architect. Students can visit NIT Trichy, IIT Kharagpur, JMI New Delhi

3 Jobs Available
##### Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
##### Bank Probationary Officer (PO)

A career as Bank Probationary Officer (PO) is seen as a promising career opportunity and a white-collar career. Each year aspirants take the Bank PO exam. This career provides plenty of career development and opportunities for a successful banking future. If you have more questions about a career as  Bank Probationary Officer (PO), what is probationary officer or how to become a Bank Probationary Officer (PO) then you can read the article and clear all your doubts.

3 Jobs Available
##### Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

3 Jobs Available
##### Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
##### Finance Executive

A career as a Finance Executive requires one to be responsible for monitoring an organisation's income, investments and expenses to create and evaluate financial reports. His or her role involves performing audits, invoices, and budget preparations. He or she manages accounting activities, bank reconciliations, and payable and receivable accounts.

3 Jobs Available
##### Investment Banker

An Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.

3 Jobs Available
##### Bank Branch Manager

Bank Branch Managers work in a specific section of banking related to the invention and generation of capital for other organisations, governments, and other entities. Bank Branch Managers work for the organisations and underwrite new debts and equity securities for all type of companies, aid in the sale of securities, as well as help to facilitate mergers and acquisitions, reorganisations, and broker trades for both institutions and private investors.

3 Jobs Available
##### Treasurer

Treasury analyst career path is often regarded as certified treasury specialist in some business situations, is a finance expert who specifically manages a company or organisation's long-term and short-term financial targets. Treasurer synonym could be a financial officer, which is one of the reputed positions in the corporate world. In a large company, the corporate treasury jobs hold power over the financial decision-making of the total investment and development strategy of the organisation.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

3 Jobs Available
##### Construction Manager

Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.

2 Jobs Available
##### Carpenter

Carpenters are typically construction workers. They stay involved in performing many types of construction activities. It includes cutting, fitting and assembling wood.  Carpenters may help in building constructions, bridges, big ships and boats. Here, in the article, we will discuss carpenter career path, carpenter salary, how to become a carpenter, carpenter job outlook.

2 Jobs Available
##### Welder

An individual who opts for a career as a welder is a professional tradesman who is skilled in creating a fusion between two metal pieces to join it together with the use of a manual or fully automatic welding machine in their welder career path. It is joined by intense heat and gas released between the metal pieces through the welding machine to permanently fix it.

2 Jobs Available
##### Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.

2 Jobs Available
##### Naval Architect

A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability.

2 Jobs Available
##### Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.

2 Jobs Available
##### Field Surveyor

Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials.

2 Jobs Available
##### Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

6 Jobs Available
##### Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

5 Jobs Available
##### Veterinary Doctor

A veterinary doctor is a medical professional with a degree in veterinary science. The veterinary science qualification is the minimum requirement to become a veterinary doctor. There are numerous veterinary science courses offered by various institutes. He or she is employed at zoos to ensure they are provided with good health facilities and medical care to improve their life expectancy.

5 Jobs Available
##### Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.

4 Jobs Available
##### Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

3 Jobs Available
##### Surgical Technologist

When it comes to an operation theatre, there are several tasks that are to be carried out before as well as after the operation or surgery has taken place. Such tasks are not possible without surgical tech and surgical tech tools. A single surgeon cannot do it all alone. It’s like for a footballer he needs his team’s support to score a goal the same goes for a surgeon. It is here, when a surgical technologist comes into the picture. It is the job of a surgical technologist to prepare the operation theatre with all the required equipment before the surgery. Not only that, once an operation is done it is the job of the surgical technologist to clean all the equipment. One has to fulfil the minimum requirements of surgical tech qualifications.

3 Jobs Available
##### Critical Care Specialist

A career as Critical Care Specialist is responsible for providing the best possible prompt medical care to patients. He or she writes progress notes of patients in records. A Critical Care Specialist also liaises with admitting consultants and proceeds with the follow-up treatments.

2 Jobs Available
##### Ophthalmologist

Individuals in the ophthalmologist career in India are trained medically to care for all eye problems and conditions. Some optometric physicians further specialize in a particular area of the eye and are known as sub-specialists who are responsible for taking care of each and every aspect of a patient's eye problem. An ophthalmologist's job description includes performing a variety of tasks such as diagnosing the problem, prescribing medicines, performing eye surgery, recommending eyeglasses, or looking after post-surgery treatment.

2 Jobs Available
##### Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.

4 Jobs Available
##### Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
##### Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages. Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
##### Talent Agent

The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

3 Jobs Available

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
##### Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
##### Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
##### Talent Director

Individuals who opt for a career as a talent director are professionals who work in the entertainment industry. He or she is responsible for finding out the right talent through auditions for films, theatre productions, or shows. A talented director possesses strong knowledge of computer software used in filmmaking, CGI and animation. A talent acquisition director keeps himself or herself updated on various technical aspects such as lighting, camera angles and shots.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. Ever since internet cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.

3 Jobs Available
##### Travel Journalist

The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.

2 Jobs Available
##### Videographer

Careers in videography are art that can be defined as a creative and interpretive process that culminates in the authorship of an original work of art rather than a simple recording of a simple event. It would be wrong to portrait it as a subcategory of photography, rather photography is one of the crafts used in videographer jobs in addition to technical skills like organization, management, interpretation, and image-manipulation techniques. Students pursue Visual Media, Film, Television, Digital Video Production to opt for a videographer career path. The visual impacts of a film are driven by the creative decisions taken in videography jobs. Individuals who opt for a career as a videographer are involved in the entire lifecycle of a film and production.

2 Jobs Available
##### SEO Analyst

An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.

2 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
##### Production Manager

Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers.

3 Jobs Available

A Team Leader is a professional responsible for guiding, monitoring and leading the entire group. He or she is responsible for motivating team members by providing a pleasant work environment to them and inspiring positive communication. A Team Leader contributes to the achievement of the organisation’s goals. He or she improves the confidence, product knowledge and communication skills of the team members and empowers them.

2 Jobs Available
##### Quality Systems Manager

A Quality Systems Manager is a professional responsible for developing strategies, processes, policies, standards and systems concerning the company as well as operations of its supply chain. It includes auditing to ensure compliance. It could also be carried out by a third party.

2 Jobs Available
##### Merchandiser

A career as a merchandiser requires one to promote specific products and services of one or different brands, to increase the in-house sales of the store. Merchandising job focuses on enticing the customers to enter the store and hence increasing their chances of buying a product. Although the buyer is the one who selects the lines, it all depends on the merchandiser on how much money a buyer will spend, how many lines will be purchased, and what will be the quantity of those lines. In a career as merchandiser, one is required to closely work with the display staff in order to decide in what way a product would be displayed so that sales can be maximised. In small brands or local retail stores, a merchandiser is responsible for both merchandising and buying.

2 Jobs Available
##### Procurement Manager

The procurement Manager is also known as  Purchasing Manager. The role of the Procurement Manager is to source products and services for a company. A Procurement Manager is involved in developing a purchasing strategy, including the company's budget and the supplies as well as the vendors who can provide goods and services to the company. His or her ultimate goal is to bring the right products or services at the right time with cost-effectiveness.

2 Jobs Available
##### Production Planner

Individuals who opt for a career as a production planner are professionals who are responsible for ensuring goods manufactured by the employing company are cost-effective and meets quality specifications including ensuring the availability of ready to distribute stock in a timely fashion manner.

2 Jobs Available
##### ITSM Manager

ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.

3 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### IT Consultant

An IT Consultant is a professional who is also known as a technology consultant. He or she is required to provide consultation to industrial and commercial clients to resolve business and IT problems and acquire optimum growth. An IT consultant can find work by signing up with an IT consultancy firm, or he or she can work on their own as independent contractors and select the projects he or she wants to work on.

2 Jobs Available
##### Data Architect

A Data Architect role involves formulating the organisational data strategy. It involves data quality, flow of data within the organisation and security of data. The vision of Data Architect provides support to convert business requirements into technical requirements.

2 Jobs Available
##### Security Engineer

The Security Engineer is responsible for overseeing and controlling the various aspects of a company's computer security. Individuals in the security engineer jobs include developing and implementing policies and procedures to protect the data and information of the organisation. In this article, we will discuss the security engineer job description, security engineer skills, security engineer course, and security engineer career path.

2 Jobs Available
##### UX Architect

A UX Architect is someone who influences the design processes and its outcomes. He or she possesses a solid understanding of user research, information architecture, interaction design and content strategy.

2 Jobs Available