Q. 1503.7( 3 Votes )

# In Fig. 6.51, PQ = PS and ∠1 = ∠2.

(i) Is ∆PQR ≅ ∆PSR? Give reasons.

(ii) Is QR = SR? Give reasons.

Answer :

Given: PQ = PS and ∠1 = ∠2

**Formula Used/Theory:-**

→ when 2 sides and angle between both the sides are equal in both the triangles then triangles are congruent by SAS congruence criterion

In Δ PQR and Δ PSR

PQ = PS (Given)

PR = PR (Common)

∠QPR = ∠SPR (Given)

∴ ∆PQR ≅ ∆PSR

Hence; Δ PQR and Δ PSR are congruent by SAS criterion

If ∆PQR ≅ ∆PSR then;

All 6 perimeters are equal.

PQ = PS; PR = PR; QR = SR

∠1 = ∠2; ∠Q = ∠S; ∠PRQ = ∠PRS

Rate this question :

Complete the congruence statement:

?

?

NCERT MathematicsIn the figure, the two triangles are congruent. The corresponding parts are marked. We can write ?

NCERT Mathematics

Triangles DEF and LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = MN, then, are the two triangles congruent? Which condition do you use?

If ∠E = 40°, what is the measure of ∠N?

NCERT - Exemplar MathematicsIn Fig. 6.53, ∠1 = ∠2 and ∠3 = ∠4.

(i) Is ∆ADC ≅ ∆ABC? Why?

(ii) Show that AD = AB and CD = CB.

NCERT - Exemplar Mathematics

In Fig. 6.52, DE = IH, EG = FI and ∠E = ∠I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion?

NCERT - Exemplar Mathematics

In Fig. 6.51, PQ = PS and ∠1 = ∠2.

(i) Is ∆PQR ≅ ∆PSR? Give reasons.

(ii) Is QR = SR? Give reasons.

NCERT - Exemplar MathematicsIn Fig. 6.50, which pairs of triangles are congruent by SAS congruence criterion (condition)? If congruent, write the congruence of the two triangles in symbolic form.

NCERT - Exemplar Mathematics