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.