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Question
If ΔPQR and ΔSOR are both isosceles triangle on a common base OR such that P and S lie on the same side of QR. Are triangles PSQ and PSR congruent? Which condition do you use?
Solution
Let ∆PQR and ∆SOR are the given triangles such that PQ = PR and SQ = SR.
Now, in ∆PSQ and ∆PSR,
PQ = PR ......(Given)
SQ = SR ......(Given)
PS = PS ......(Common)
∴ ∆PSQ ≅ ∆PSR ......(SSS criterion)
Yes, the ∆PSQ and ∆PSR are congruent by using SSS criterion
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