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Question

In the figure, PQRS is a square and SRT is an equilateral triangle. Prove that

(i) PT = QT (ii) TQR=15

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Solution

Given: PQRS is a square and SRT is an equilateral triangle. PT and QT are joined.

To prove : (i) PT = QT; (ii) TQR=15

Proof : In ΔTSP and ΔTQR

ST = RT (Sides of equilateral triangle)

SP = RQ (Sides of square)

and TSP=TRQ (Each=60+90)

ΔTSP ΔTQR (SAS axiom)

PT=QT (c.p.c.t.)

In ΔTQR,

RT=RQ (Square sides)

RTQ=RQT

But TRQ=60+90=150

RTQ+RQT=180150=30

PTQ=RQT (Proved)

RQT=302=15

TQR=15


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