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NCERT Solutions for Exercise 6.1 Class 10 Maths Chapter 6 - Triangles

NCERT Solutions for Exercise 6.1 Class 10 Maths Chapter 6 - Triangles

Updated on Apr 29, 2025 05:37 PM IST | #CBSE Class 10th

A triangle is a polygon that has three sides and three corners. It is one of the basic geometrical shapes with a minimum number of lines polygon. For comparing and describing triangles congruence property is used. Two triangles are said to be congruent if they are identical in terms of their shape and size. But not all the figures or shape that has similar shape or size need to be congruent. In other words, triangles are said to be congruent if the corresponding sides or angles of one shape are equal to the corresponding sides or angles of the other triangle.

This Story also Contains
  1. Download Free Pdf of NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.1
  2. Assess NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.1
  3. Topics Covered in Chapter 6, Triangles: Exercise 6.1
  4. NCERT Solutions Subject Wise
  5. Subject-Wise NCERT Exemplar Solutions
NCERT Solutions for Exercise 6.1 Class 10 Maths Chapter 6 - Triangles
NCERT Solutions for Exercise 6.1 Class 10 Maths Chapter 6 - Triangles

NCERT solutions of Class 10 maths ex 6.1 concentrate on triangles and their similarity and congruence concept. Here we will discover the meaning of comparable triangles, and learn how comparable geometric forms differ and why they're grouped together. These distinctions between similar geometric shapes will aid your understanding of how these triangles differ. NCERT solutions for exercise 6.1 Class 10 Maths chapter 6 Triangles discuss the concept of geometry as per the NCERT Book, which helps us to grasp new ideas in advanced classes.

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Download Free Pdf of NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.1

Download PDF

Assess NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.1

Q1 (1) Fill in the blanks using the correct word given in brackets: All circles are ______ . (congruent, similar)

Answer:

All circles are similar.

Since all the circles have a similar shape. They may have different radii, but the shape of all circles is the same.

Therefore, all circles are similar.

Q1 (2) Fill in the blanks using the correct word given in brackets: All squares are ______. (similar, congruent)

Answer:

All squares are similar.

Since all the squares have a similar shape. They may have a different side, but the shape of all squares is the same.

Therefore, all squares are similar.

Q1 (3) Fill in the blanks using the correct word given in brackets: All ______triangles are similar. (isosceles, equilateral)

Answer:

All equilateral triangles are similar.

Since all the equilateral triangles have a similar shape. They may have different sides but the shape of all equilateral triangles is the same.

Therefore, all equilateral triangles are similar.

Q1 (4) Fill in the blanks using the correct word given in brackets : (iv) Two polygons of the same number of sides are similar if(a) there corresponding angles are _________and (b) their corresponding sides are________. (equal, proportional)

Answer:

Two polygons of the same number of sides are similar if their corresponding angles are equal and their corresponding sides are proportional.

Thus, (a) equal

(b) proportional

Q2 (1) Give two different examples of a pair of similar figures.

Answer:

The two different examples of a pair of similar figures are :

1. Two circles with different radii.

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2. Two rectangles with different breadth and length.

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Q2 (2) Give two different examples of a pair of non-similar figures.

Answer:

The two different examples of a pair of non-similar figures are :

1. Rectangle and circle

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2. A circle and a triangle.

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Q3 State whether the following quadrilaterals are similar or not:

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Answer:

Quadrilateral PQRS and ABCD are not similar as their corresponding sides are proportional, i.e. 1:2, but their corresponding angles are not equal.

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Topics Covered in Chapter 6, Triangles: Exercise 6.1

1. Definition of Triangle: A triangle is a polygon that has three edges and three vertices. It means the polygon with the minimum number of sides is called a triangle. To understand the terms related to triangles student must know the basic definition of a triangle.

2. Congruent Triangles: This is the basic concept that is used to compare triangles. Two triangles are said to be congruent if they same size and shape. Two criteria for triangle congruence are as follows -

  • Their corresponding angles are equal and

  • Their corresponding sides are in the same ratio.

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3. Similar Figure: Two triangles or any other figure are said to be similar if they have the same shape, but not necessarily have the same size. For example, two equilateral triangles in which each side of the first triangle is 6cm and each side of the other triangle is 8cm are said to be similar because both are equilateral triangles.

Also see-

JEE Main Important Mathematics Formulas

As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

NCERT Solutions Subject Wise

Students must check the NCERT solutions for Class 10 Maths and Science given below:

Subject-Wise NCERT Exemplar Solutions

Students must check the NCERT exemplar solutions for Class 10 Maths and Science given below:

Frequently Asked Questions (FAQs)

1. Can a triangle and square be similar to each other?

No, because they have different number of sides. Triangle has three and square has 4


2. What are similar figures?

Two figures are similar to each other if they have the same shape but are of different size.


3. What is the sum of all the angels of a triangle?

Sum of the angels of a triangle is 180 degrees. 


4. What are the conditions for two figures to be similar according to NCERT Solutions for Class 10 Maths Exercise 6.1?

Two figures with same number of sides are similar if 

  1. their corresponding angles are equal and 

  2. their corresponding sides are in the same ratio, 


5. Can two circles of any radius be similar to each other?

Yes, any two given circles are always similar to each other.


6. Why can’t a rectangle and a square be similar to each other?

Because, the sides of rectangle are not equal to each other. Thus, the ratio of sides is not same for all the sides.


7. Does similarity mean the figures are congruent?

No, similarity means that the figures are just of same shape it doesn’t mean that they are equal.


8. Can we proof that any two regular polygons of same side are similar to each other?

Yes, if their number of sides are equal to each other then the two are similar.

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Questions related to CBSE Class 10th

Have a question related to CBSE Class 10th ?

Hello

Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.

1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.

2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.

3. Counseling and Seat Allocation:

After the KCET exam, you will need to participate in online counseling.

You need to select your preferred colleges and courses.

Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.

4. Required Documents :

Domicile Certificate (proof that you are a resident of Karnataka).

Income Certificate (for minority category benefits).

Marksheets (11th and 12th from the Karnataka State Board).

KCET Admit Card and Scorecard.

This process will allow you to secure a seat based on your KCET performance and your category .

check link for more details

https://medicine.careers360.com/neet-college-predictor

Hope this helps you .

Hello Aspirant,  Hope your doing great,  your question was incomplete and regarding  what exam your asking.

Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.

hello Zaid,

Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.

best of luck!

According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.

You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

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

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