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?

Answer 1

Let ∆PQR and ∆SQR 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.