Q. 1475.0( 2 Votes )
If ∆PQR and ∆SQR are both isosceles triangle on a common base QR such that P and S lie on the same side of QR. Are triangles PSQ and PSR congruent? Which condition do you use?
Answer :
Given: ∆PQR and ∆SQR are both isosceles triangle on a common
base QR
Formula Used/Theory:-
→ 2 sides of triangle are equal gives a isosceles triangle
→ If all sides of triangle are equal to all other sides of triangle
Then both triangle are congruent by SSS criterion
As ∆PQR and ∆SQR are both isosceles triangle on a common base QR
Then;
PQ = PR and SQ = SR
In Δ PSQ and Δ PSR
SQ = SR (stated above)
PQ = PR (stated above)
PS = PS (common)
∴ Δ PSQ ≅ Δ PSR
Hence; both triangles PSQ and PSR are congruent by SSS criterion
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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.
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(i) Is ∆PQR ≅ ∆PSR? Give reasons.
(ii) Is QR = SR? Give reasons.
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