Question

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

Answer 1

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,

→ ∠QRS = (x + y) = 90° . (Proved.)