Question

In figure, PQRS is a square and SRT is an equilateral triangle. Prove that :
(1) PT=QT
(2)<TQR = 15°

Pls give me answer with proof
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Answer 1

Answer:#BAL

Step-by-step explanation:

Since PQRS is a square

Therefore all sides are equal

and all angles are equal to 90.

Since triangle SRT is equilateral

Therefore all sides are equal

and all angles are equal to 60.

Therefore, SP=SR=ST=RQ=SR=TR

We know that angle opposite to equal sides are equal

Therefore,<STP=<SPT --------(1)

<QTR=<TQR----------(2)

Now, In triangle STP and triangleQTR

TS=TR

PS=RQ

<TSP=<TRS (<PSR +<TSR=

<QRS+<TRS)

Therefore triangle STP congruent triangle QTR

By CPCT

PT=QT

In triangle TRQ

<TRQ+<RQT+<RTQ=180

<QRS+<TRS+2 <RQT=180

90+60+2 <RQT=180

150+2 <RQT=180

2 <RQT=180-150

2 <RQT=30

<RQT=30/2=15