Question

In the given figure PQR is an equilateral triangle and QRST is a square.Prove that (i) PT=PS (ii) angel PSR=15 degree​

Answer 1

Answer:

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Step-by-step explanation:

so as here QRST is a square.

QT=TS=SR=QR (1)

also here PQR is an equilateral triangle

so thus then

PQ=QR=PR (2)

Moreover Angle PQR=angle QPR=Angle PRQ=60 degrees (3)

similarly Angle QTS=Angle TSR=Angle RQT=Angle QRS=90 degree (4)

so from (1) and (2)

we get PR=RS

thus Angle RPS=Angle RSP,, (5)

by converse of isosceles triangle theorem

So now considering triangle TQR & triangle PRS

so PQ=PR

QT=RS from (1) and (2)

so Angle QPT=Angle RPS [common angle]

thus triangle QPT congruent to triangle PRS by SAS Test

thus PT=TS (c.s.c.t)

thus proved

now thus by angle addition property

we get Angle PRS=angleAngle QRS+Angle PRQ=90+60=150 (6)

thus considering triangle PRS

Angle PRS+Angle RPS+Angle RSP=180

so 2Angle PSR+150=180 from (5) and (6)

thus angle 2Angle PSR=30

Ie Angle PSR=15 Degrees

thus proved