NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles are given here. Students can either practice online or download these files and practice different types of questions related to this chapter and thereby achieve maximum marks in their examinations. The relation of two objects being congruent is called congruence. Subject experts prepare these NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles carefully, without any mistakes.

Chapter 7 – Congruence of Triangles contains 2 exercises. Let us have a look at some of the concepts discussed in this chapter.

  • Congruence of Plane Figures
  • Congruence Among Line Segments
  • Congruence of Angles
  • Congruence of Triangles
  • Criteria For Congruence of Triangles
  • Congruence Among Right-Angled Triangles

Download the PDF of NCERT Solutions For Class 7 Maths Chapter 7 Congruence of Triangles

 

ncert sol class 7 math ch 7 ex 1
ncert sol class 7 math ch 7 ex 1
ncert sol class 7 math ch 7 ex 2
ncert sol class 7 math ch 7 ex 2
ncert sol class 7 math ch 7 ex 2
ncert sol class 7 math ch 7 ex 2
ncert sol class 7 math ch 7 ex 2
ncert sol class 7 math ch 7 ex 2
ncert sol class 7 math ch 7 ex 2
ncert sol class 7 math ch 7 ex 2

Access exercises of NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles

Exercise 7.1 Solutions

Exercise 7.2 Solutions

Access answers to Maths NCERT Solutions For Class 7 Chapter 7 – Congruence of Triangles

Exercise 7.1 Page: 137

1. Complete the following statements:

(a) Two line segments are congruent if ___________.

Solution:-

Two line segments are congruent if they have the same length.

(b) Among two congruent angles, one has a measure of 70o; the measure of the other angle is ___________.

Solution:-

Among two congruent angles, one has a measure of 70o; the measure of the other angle is 70o.

Because, if two angles have the same measure, they are congruent. Also, if two angles are congruent, their measure are same.

(c) When we write ∠A = ∠B, we actually mean .

Solution:-

When we write ∠A = ∠B, we actually mean m ∠A = m ∠B.

2. Give any two real-life examples for congruent shapes.

Solution:-

The two real-life example for congruent shapes are,

(i) Fan feathers of same brand.

(ii) Size of chocolate in the same brand.

(iii) Size of pens in the same brand

3. If ΔABC ≅ ΔFED under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.

Solution:-

Two triangles are congruent if pairs of corresponding sides and corresponding angles are equal.

All the corresponding congruent parts of the triangles are,

∠A ↔ ∠F, ∠B ↔ ∠E, ∠C ↔ ∠D

Correspondence between sides:

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 1

4. If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to

(i) ∠E (ii) NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 2 (iii) ∠F (iv) NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 3

Solution:-

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 4

From above the figure we can say that,

The part(s) of ΔBCA that correspond to,

(i) ∠E ↔ ∠C

(ii)
NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 5

(iii) ∠F ↔ ∠A

(iv)
NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 6


Exercise 7.2 Page: 149

1. Which congruence criterion do you use in the following?

(a) Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 7

Solution:-

By SSS congruence property:- Two triangles are congruent if the three sides of one triangle are respectively equal to the three sides of the other triangle.

ΔABC ≅ ΔDEF

(b) Given: ZX = RP

RQ = ZY

∠PRQ = ∠XZY

So, ΔPQR ≅ ΔXYZ

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 8

Solution:-

By SAS congruence property:- Two triangles are congruent if the two sides and the included angle of one are respectively equal to the two sides and the included angle of the other.

ΔACB ≅ ΔDEF

(c) Given: ∠MLN = ∠FGH

∠NML = ∠GFH

∠ML = ∠FG

So, ΔLMN ≅ ΔGFH

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 9

Solution:-

By ASA congruence property:- Two triangles are congruent if the two angles and the included side of one are respectively equal to the two angles and the included side of the other.

ΔLMN ≅ ΔGFH

(d) Given: EB = DB

AE = BC

∠A = ∠C = 90o

So, ΔABE ≅ ΔACD

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 10

Solution:-

By RHS congruence property:- Two right triangles are congruent if the hypotenuse and one side of the first triangle are respectively equal to the hypotenuse and one side of the second.

ΔABE ≅ ΔACD

2. You want to show that ΔART ≅ ΔPEN,

(a) If you have to use SSS criterion, then you need to show

(i) AR = (ii) RT = (iii) AT =

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 11

Solution:-

We know that,

SSS criterion is defined as, two triangles are congruent if the three sides of one triangle are respectively equal to the three sides of the other triangle.

∴ (i) AR = PE

(ii) RT = EN

(iii) AT = PN

(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have

(i) RT = and (ii) PN =

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 12

Solution:-

We know that,

SAS criterion is defined as, two triangles are congruent if the two sides and the included angle of one are respectively equal to the two sides and the included angle of the other.

∴ (i) RT = EN

(ii) PN = AT

(c) If it is given that AT = PN and you are to use ASA criterion, you need to have

(i) ? (ii) ?

Solution:-

We know that,

ASA criterion is defined as, two triangles are congruent if the two angles and the included side of one are respectively equal to the two angles and the included side of the other.

Then,

(i) ∠ATR = ∠PNE

(ii) ∠RAT = ∠EPN

3. You have to show that ΔAMP ≅ ΔAMQ.

In the following proof, supply the missing reasons.

Steps Reasons
(i) PM = QM (i) …
(ii) ∠PMA = ∠QMA (ii) …
(iii) AM = AM (iii) …
(iv) ΔAMP ≅ ΔAMQ (iv) …

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 13

Solution:-

Steps Reasons
(i) PM = QM (i) From the given figure
(ii) ∠PMA = ∠QMA (ii) From the given figure
(iii) AM = AM (iii) Common side for the both triangles
(iv) ΔAMP ≅ ΔAMQ (iv) By SAS congruence property:- Two triangles are congruent if the two sides and the included angle of one are respectively equal to the two sides and the included angle of the other.

4. In ΔABC, ∠A = 30o, ∠B = 40o and ∠C = 110o

In ΔPQR, ∠P = 30o, ∠Q = 40o and ∠R = 110o

A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or Why not?

Solution:-

No, because the two triangles with equal corresponding angles need not be congruent. In such a correspondence, one of them can be enlarged copy of the other.

5. In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ΔRAT ≅ ?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 14

Solution:-

From the given figure,

We may observe that,

∠TRA = ∠OWN

∠TAR = ∠NOW

∠ATR = ∠ONW

Hence, ΔRAT ≅ ΔWON

6. Complete the congruence statement:

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 15

ΔBCA ≅ ΔQRS ≅

Solution:-

First consider the ΔBCA and ΔBTA

From the figure, it is given that,

BT = BC

Then,

BA is common side for the ΔBCA and ΔBTA

Hence, ΔBCA ≅ ΔBTA

Similarly,

Consider the ΔQRS and ΔTPQ

From the figure, it is given that

PT = QR

TQ = QS

PQ = RS

Hence, ΔQRS ≅ ΔTPQ

7. In a squared sheet, draw two triangles of equal areas such that

(i) The triangles are congruent.

(ii) The triangles are not congruent.

What can you say about their perimeters?

Solution:-

(ii)

 

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 16

In the above figure, ΔABC and ΔDEF have equal areas.

And also, ΔABC ≅ ΔDEF

So, we can say that perimeters of ΔABC and ΔDEF are equal.

(ii)

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 17

In the above figure, ΔLMN and ΔOPQ

ΔLMN is not congruent to ΔOPQ

So, we can also say that their perimeters are not same.

8. Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.

Solution:-

Let us draw triangles LMN and FGH.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 18

In the above figure, all angles of two triangles are equal. But, out of three sides only two sides are equal.

Hence, ΔLMN is not congruent to ΔFGH.

9. If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 19

Solution:-

By observing the given figure, we can say that

∠ABC = ∠PQR

∠BCA = ∠PRQ

The other additional pair of corresponding part is BC = QR

∴ ΔABC ≅ ΔPQR

10. Explain, why ΔABC ≅ ΔFED

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Image 20

Solution:-

From the figure, it is given that,

∠ABC = ∠DEF = 90o

∠BAC = ∠DFE

BC = DE

By ASA congruence property, two triangles are congruent if the two angles and the included side of one are respectively equal to the two angles and the included side of the other.

ΔABC ≅ ΔFED


 

Leave a Comment

Your email address will not be published. Required fields are marked *