Question

Q.4. APQR is an isosceles triangle in which PQ=PR Side QP is produced to S
such that PS= PQ (see figure). Show that ZQRS is a right angle. [5 Marks]
S
P
Q
11.​

Answer 1

Given :

• ∆PQR is an isosceles triangle in which PQ = PR.
• Side OP 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.)

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