# NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles  Written by Team Trustudies
Updated at 2021-05-07

## NCERT solutions for class 7 Maths Chapter 7 Congruence Of Triangles Exercise 7.1

Q.1 Complete the following statements:
(a) Two line segments are congruent if _______ .
(b) Among the congruent angles, one has a measure of 70°, the measure of the other angle is _______ .
(c) When we write $$\angle A = \angle B$$, we actually mean

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(a) Two line segments are congruent if _they have the same length_ .
(b) Among the congruent angles, one has a measure of 70°, the measure of the other angle is _70°_ .
(c) $$m \angle A = m \angle B$$

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

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

Chocolate of the same packets.
Mobile phone of the same brand and model

Q.3 If $$\triangle ABC \cong \triangle FED$$ under the correspondence ABC ? FED, write all the corresponding congruent parts of the triangles.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

Given: $$\triangle ABC \cong \triangle FED$$ and ABC? FED $$\therefore$$ $$\overline{AB}?\overline{FE}, \overline{BC}?\overline{ED}, \overline{AC}?\overline{FD}$$
$$\angle A?\angle F, \angle B?\angle E,\angle C?\angle D$$

Q.4 If $$\triangle DEF \cong \triangle BCA.$$ Write the part of ABCA that correspond to
(i) $$\angle E$$
(ii) $$\overline EF$$
(iii) $$\angle F$$
(iv) $$\overline DF$$

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

Given: $$\triangle DEF \cong \triangle BCA.$$
(i) $$\angle E ? \angle C$$
(ii) $$\angle F ? \angle A$$
(iii) EF ? ZA
(iv) DF ? BA

## NCERT solutions for class 7 Maths Chapter 7 Congruence Of Triangles Exercise 7.2

Q.1 Which congruence criterion do you use in the following?
(a) Given:
AC = DF
AB = DE
BC = EF
So, $$\triangle ABC \cong \triangle DEF$$ (b) Given:
ZX = RP
RQ = ZY
$$\angle PRQ = \angle XZY$$
So, $$\triangle PQR \cong \triangle XYZ$$ (c) Given: $$\angle MLN = \angle FGH$$
$$\angle NML = \angle GFH$$
ML = FG
So, $$\triangle LMN \cong \triangle GFH$$ (d) Given: EB = DB
AE = BC
$$\angle A = \angle C = 90°$$
So, $$\triangle ABE \cong \triangle CDB$$ NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(a) $$\triangle ABC \cong \triangle DEF$$ (BY SSS rule)
(b) $$\triangle PQR \cong \triangle XYZ$$ (BY SAS rule)
(c) $$\triangle LMN \cong \triangle GFH$$ (BY ASA rule)
(d) $$\triangle ABE \cong \triangle CDB$$ (BY RHS rule)

Q.2 You want to show that $$\triangle ART = \triangle PEN,$$ (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) ?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(a) For SSS criterion, we need
(i) AR = PE
(ii) RT = EN
(iii) AT = PN
(b) For SAS criterion, we need
(i) RT = EN and
(ii) PN = AT
(c) For ASA criterion, we need
(i) $$\angle A = \angle P$$ (ii) $$\angle T = \angle N$$

Q.3 You have to show that $$\triangle AMP \cong \triangle AMQ$$. In the fallowing proof, supply the missing reasons.  NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles Q.4 In ?ABC, $$\angle A = 30° \angle B = 40° and \angle C = 110°$$
In $$\triangle PQR, \angle P = 30°, \angle Q = 40° and \angle R = 110°.$$
A student says that $$\triangle ABC = \triangle PQR$$ by AAA congruence criterion.
Is he justified? Why or why not?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

The student is not justified because there is not criterion for AAA congruence rule.

Q.5 In the figure, the two triangles are congruent. The corresponding parts are marked. We can write $$\triangle RAT \cong$$ ? NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

In $$\triangle RAT and \triangle WON$$
AT=ON (Given)
AR=OW (Given)
$$\angle A = \angle O$$ (Given)
$$\therefore \triangle RAT \cong \triangle WON$$(By SAS rule)

Q.6 Complete the congruence statement: $$\triangle BCA \cong ? \triangle QRS \cong ?$$

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(i) In $$\triangle BCA and \triangle BTA$$
BC = BT (Given)
$$\angle CBA= \angle TBA (Given)$$
BA= BA (Common)
$$\therefore \triangle BCA = \triangle BTA$$ (by SAS rule)
(ii) In $$\triangle QRS and \triangle TPQ$$
RS = PQ (Given)
QS =TQ (Given)
PT= QR (Given)
$$\triangle QRS \cong \triangle TPQ$$ (by AAA rule)

Q.7 In a squared sheet, draw two triangles of equal areas such that:
(i) the triangles are congruent.
(ii) the triangle are not congruent.
What can you say about their perimeters?

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

(i) i.e. perimeter of $$\triangle ART$$= Perimeter of $$\triangle PEN$$
(ii) Perimeter of $$\triangle ABC \neq$$ Perimeter of $$\triangle PQR$$

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

NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles Q.9 If $$\triangle ABC and \triangle PQR$$ 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

In $$\triangle ABC and \triangle PQR$$
$$\angle ABC = \angle PQR$$
$$\angle BCA = \angle PRQ$$
The other additional pair of corresponding part is BC = QR
$$\therefore \triangle ABC \cong \triangle PQR$$

Q.10 Explain, why $$\triangle ABC \cong \triangle FED$$ NCERT Solutions for Class 7 Maths Chapter 7 Congruence Of Triangles

In $$\triangle ABC and \triangle FED$$
$$\angle B = \angle E = 90°$$ (Given)
$$\angle A = \angle F$$ (Given)
$$\therefore \angle A + \angle B = \angle E + \angle F$$
$$180° – \angle C = 180° – \angle D$$
[Angle sum property of triangles]
$$\therefore \angle C =\angle D$$
BC = ED (Given)
$$\therefore \triangle ABC = \triangle FED$$ (By ASA rule)

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