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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