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

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

#CBSE Class 10th
Updated on 02 Jun 2025, 02:37 PM IST

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

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

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.

1635922757481

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.

1635922838551

Q3 State whether the following quadrilaterals are similar or not:

1745663209508

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.

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-

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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)

Q: Can a triangle and square be similar to each other?
A:

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


Q: What are similar figures?
A:

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


Q: What is the sum of all the angels of a triangle?
A:

Sum of the angels of a triangle is 180 degrees. 


Q: What are the conditions for two figures to be similar according to NCERT Solutions for Class 10 Maths Exercise 6.1?
A:

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, 


Q: Can two circles of any radius be similar to each other?
A:

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


Q: Why can’t a rectangle and a square be similar to each other?
A:

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


Q: Does similarity mean the figures are congruent?
A:

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


Q: Can we proof that any two regular polygons of same side are similar to each other?
A:

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

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Have a question related to CBSE Class 10th ?
25.05.2013 date of birth and i am studying in class 9th therefore I can gives the CBSE board exam on 2027....

Hello,

Yes, you can give the CBSE board exam in 2027.

If your date of birth is 25.05.2013, then in 2027 you will be around 14 years old, which is the right age for Class 10 as per CBSE rules. So, there is no problem.

Hope it helps !

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Prachi Kumari
27 Aug'25
My school has asked to create apaar id.. but I selected none and forgot to put CBSE as institution will it affect any way?

Hello! If you selected “None” while creating your APAAR ID and forgot to mention CBSE as your institution, it may cause issues later when linking your academic records or applying for exams and scholarships that require school details. It’s important that your APAAR ID correctly reflects your institution to avoid verification problems. You should log in to the portal and update your profile to select CBSE as your school. If the system doesn’t allow editing, contact your school’s administration or the APAAR support team immediately so they can correct it for you.

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Chelsie G
23 Aug'25
i want to know my class 10th registration number

Hello Aspirant,

Here's how you can find it:

  • School ID Card: Your registration number is often printed on your school ID card.

  • Admit Card (Hall Ticket): If you've received your board exam admit card, the registration number will be prominently displayed on it. This is the most reliable place to find it for board exams.

  • School Records/Office: The easiest and most reliable way is to contact your school office or your class teacher. They have access to all your official records and can provide you with your registration number.

  • Previous Mark Sheets/Certificates: If you have any previous official documents from your school or board (like a Class 9 report card that might have a student ID or registration number that carries over), you can check those.

Your school is the best place to get this information.

Read Complete Answer
S
SHUBHRADIP ROY
20 Aug'25
Currently I passed my 10 in 2024-2025 session can I fill form

Hello,

It appears you are asking if you can fill out a form after passing your 10th grade examination in the 2024-2025 academic session.

The answer depends on what form you are referring to. Some forms might be for courses or examinations where passing 10th grade is a prerequisite or an eligibility criteria, such as applying for further education or specific entrance exams. Other forms might be related to other purposes, like applying for a job, which may also have age and educational requirements.

For example, if you are looking to apply for JEE Main 2025 (a competitive exam in India), having passed class 12 or appearing for it in 2025 are mentioned as eligibility criteria.

Let me know if you need imformation about any exam eligibility criteria.

good wishes for your future!!

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S
sadafreen356
20 Aug'25
CBSE board real paperAnd notes

Hello Aspirant,

"Real papers" for CBSE board exams are the previous year's question papers . You can find these, along with sample papers and their marking schemes , on the official CBSE Academic website (cbseacademic.nic.in).

For notes , refer to NCERT textbooks as they are the primary source for CBSE exams. Many educational websites also provide chapter-wise revision notes and study material that align with the NCERT syllabus. Focus on practicing previous papers and understanding concepts thoroughly.

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S
SHUBHRADIP ROY
20 Aug'25
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Popular CBSE Class 10th Questions

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

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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 :

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2.45×10−3 kg

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 6.45×10−3 kg
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 9.89×10−3 kg

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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

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

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200 \, \, J - 500 \, \, J
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2\times 10^{5}J-3\times 10^{5}J

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

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K/2\,

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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

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6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced
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33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

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67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .
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How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

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0.02

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3.125 × 10-2
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1.25 × 10-2

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2.5 × 10-2
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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

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decrease twice

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increase two fold
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remain unchanged

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be a function of the molecular mass of the substance.
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With increase of temperature, which of these changes?

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

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twice that in 60 g carbon

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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

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less than 3

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more than 3 but less than 6
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more than 6 but less than 9

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