Question

δqrs is a right triangle. select the correct similarity statement. ○ δstr ~ δtqr ○ δstr ~ δrst ○ δstr ~ δsqr ○ δstr ~ δrtq

Explanation:

In right triangle \( \triangle QRS \) (right - angled at \( R \)) and \( \triangle STR \) (right - angled at \( T \)):

1. \( \angle S \) is common to both \( \triangle STR \) and \( \triangle SQR \).
2. \( \angle STR=\angle SRQ = 90^{\circ}\) (right angles).

By the AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. So \( \triangle STR\sim\triangle SQR \) because \( \angle S=\angle S \) and \( \angle STR=\angle SRQ = 90^{\circ}\).

Answer:

\(\boldsymbol{\triangle STR\sim\triangle SQR}\)