Answer :

**To Prove: Δ PQS ∼ Δ TQRGiven: In ΔPQR,**

**∠PQR = ∠PRQ**

**Proof:**

As** **∠PQR = ∠PRQ

PQ = PR [sides opposite to equal angles are equal] (i)

Given,

by (1)

In Δ PQS and Δ TQR, we get

∠Q = ∠Q

Therefore,

By SAS similarity Rule which states that**Triangles**are

**similar**if two sides in one

**triangle**are in the

same proportion to the corresponding sides in the other, and the included angle are equal.

Δ PQS ∼ Δ TQR

Hence, Proved.

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