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
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Complete the congruence statement:
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In the figure, the two triangles are congruent. The corresponding parts are marked. We can write 
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(i) Is ∆ADC ≅ ∆ABC? Why?
(ii) Show that AD = AB and CD = CB.
In Fig. 6.52, DE = IH, EG = FI and ∠E = ∠I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion?
In Fig. 6.51, PQ = PS and ∠1 = ∠2.
(i) Is ∆PQR ≅ ∆PSR? Give reasons.
(ii) Is QR = SR? Give reasons.
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