Question

PQR is an isosceles triangle in which PQ=PR side QP is produced to S such that PS=PQ Show that QRS is a right angle​

Answer 1

Answer:

 QP is produced to such that PS= PQ Show that QRS is a right angle. 1. See answer.

Answer 2

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Given :-

∆PQR is an isosceles triangle in which PQ=PR.

Side QP is produced to such that PS = PQ.

Solution :-

Given that, PQ = PR,

So,

→ ∠PQR = ∠PRQ = Let x . (Angle Opp. to Equal sides are Equal.)

Also,

→ PS = PQ (Given.)

Than,

→ PS = PR .

So,

→ ∠PSR = ∠PRS = Let y . (Angle Opp. to Equal sides are Equal.)

Now, in ∆QRS , we have ,

→ ∠SQR + ∠QRS + ∠QSR = 180° .(Angle sum Property.)

→ x + (x + y) + y = 180°

→ 2x + 2y = 180°

→ 2(x + y) = 180°

Dividing both sides by 2,

→ (x + y) = 90°.

Hence,