Step 1: Understand the question and note down the given data

NOTE: In triangle PQR, \frac{PS}{SQ} = \frac{PT}{TR}

\angle PST = \angle PRQ

Step 2: Remember the converse of the basic the proportionality theorem

NOTE: If a line divides two sides of a triangle in the same ratio, then the

line is parallel to the third side.

EXAMPLE: In triangle PQR, \frac{PS}{SQ} = \frac{PT}{TR}

So, ST II QR

Step 3: Find the angles of the triangles

EXAMPLE: ST II QR, QP and PR are tranversals

Therefore, ∠ PST = ∠ PQR (Corresponding angles)

Also it is given that ∠ PST = ∠ PRQ

So, ∠ PRQ = ∠ PQR

Step 4: Prove that the Δ PQR is an isosceles triangle.

∠ PRQ = ∠ PQR (prove in step 3)

Therefore, PQ = PR ( sides opposite the equal angles)

So, Δ PQR is an isosceles triangle.

Hence proved.