Question

In the adjoining diagram, ST is not parallel to PQ. The necessary and sufficient conditions for ΔPQR ~ ΔTSR is:

Options

• ∠PQR = ∠STR

• ∠QPR = ∠TSR

• ∠PQR = ∠TSR

• ∠PRQ = ∠RST

Answer 1

∠PQR = ∠TSR

Explanation:

Two triangles are similar iff two pairs of corresponding angles are equal (AA criterion).

For ΔPQR ~ ΔTSR the correspondence is P↔T, Q↔S, R↔R, so the angle at P must equal the angle at T(∠QPR = ∠STR) and the angle at Q must equal the angle at S(∠PQR = ∠TSR).

This gives the required similarity.