# NCERT Solutions for Class 7 Maths Chapter 7

## Congruence of Triangles Class 7

### Exercise 7.1 : Solutions of Questions on Page Number : 137

Q1 :

Complete the following statements:

(a) Two line segments are congruent if __________.

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

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

(a) They have the same length

(b) 70°

(c) m ∠ A = m ∠ B

Q2 :

Give any two real-life examples for congruent shapes.

(i) Sheets of same letter pad

(ii) Biscuits in the same packet

Q3 :

If ΔABC ≅ ΔFED under the correspondence ABC Ã¢â€ â€ FED, write all the Corresponding congruent parts of the triangles.

Q4 :

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

(i) ∠E (ii) (iii) ∠F (iv) ### Exercise 7.2 : Solutions of Questions on Page Number : 149

Q1 :

Which congruence criterion do you use in the following?

(a) Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF (b) Given: ZX = RP

RQ = ZY

∠ PRQ = ∠ XZY

So, ΔPQR ≅ ΔXYZ (c) Given: ∠ MLN = ∠ FGH

∠ NML = ∠ GFH

ML = FG

So, ΔLMN ≅ ΔGFH (d) Given: EB = DB

AE = BC

∠ A = ∠ C = 90°

So, ΔABE ≅ ΔCDB Q2 :

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 =

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

(i) RT = and (ii) PN =

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

(i) ? (ii) ?  Q3 :

You have to show that ΔAMP ≅ AMQ.

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) … Q4 :

In ΔABC, ∠ A = 30°, ∠ B = 40° and ∠ C = 110°

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

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

Q5 :

In the figure, the two triangles are congruent.

The corresponding parts are marked. We can write ΔRAT ≅ ?  Q6 :

Complete the congruence statement:

ΔBCA ≅?

ΔQRS ≅?  Q7 :

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?

Q8 :

If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use? Q9 :

Explain, why

ΔABC ≅ ΔFED 