Question

In the given figure, if PQR is an isosceles triangle such that PQ = PR and PS = PT, then the value of y is equal to​

Answer 1

Step-by-step explanation:

In triangle PQR,

PQ=PR [Given]

= angle PRQ=angle PQR[angle opposite to the equal sides are equal]......(1)

since ST|| QR and PQ is a transversal,then

angle PQR = angle PST (corresponding angles).....(2)

since PQ || QR and PR is a transversal,then

angle PRQ=angle PST (corresponding angles).....(3)

but angle PQR = angle PRQ , then from (2) and (3) we get

angle PST = angle PTS

In triangle PST

angle PST = angle PTS (proved)

therefore PT = PS (sides opposite to equal angles are equal) 

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