Question

In the adjoining figure, PRST is a parallelogram and PT is

the median of triangle PQR. Prove that, Area of triangle PQT = Area of triangle STR.

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Answer 1

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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)

So, PT = PS (sides opposite to equal angles are equal)

Or in shorter terms,

In traingle PSR And PTS

PQ=PR (given)

RS=PT (given)

Angle A is common

So,traingles are congruent(SAS) .

So corresponding sides QT=RS