NCERT solutions for Mathematics [English] Class 7 chapter 7 - Congruence of Triangles [Latest edition]

Complete the following statement:

Two line segments are congruent if __________.

Complete the following statements:

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

Complete the following statements:

When we write ∠A = ∠ B, we actually mean __________

Give any two real-life examples for congruent shapes.

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

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

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

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

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

Which congruence criterion do you use in the following?

Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

Which congruence criterion do you use in the following?

Given: ZX = RP

RQ = ZY

∠PRQ = ∠XZY

So, ΔPQR ≅ ΔXYZ

Which congruence criterion do you use in the following?

Given: ∠MLN = ∠FGH

∠NML = ∠GFH

ML = FG

So, ΔLMN ≅ ΔGFH

Which congruence criterion do you use in the following?

Given: EB = DB

AE = BC

∠A = ∠C = 90°

So, ΔABE ≅ ΔCDB

You want to show that ΔART ≅ ΔPEN,

If you have to use SSS criterion, then you need to show

1) AR =

2) RT =

3) AT =

You want to show that ΔART ≅ ΔPEN,

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

1) RT = and

2) PN =

You want to show that ΔART ≅ ΔPEN,

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

1) ?

2) ?

You have to show that ΔAMP ≅ AMQ.

In the following proof, supply the missing reasons.

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?

In the figure, the two triangles are congruent.

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

Complete the congruence statement:

ΔBCA ≅?

ΔQRS ≅?

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

The triangles are congruent.

What can you say about their perimeters?

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

The triangles are not congruent.

What can you say about their perimeters?

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

Explain, why ΔABC ≅ ΔFED.