Question

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

Explanation:

Step1: Identify right angles

In \(\triangle STR\), \(\angle STR = 90^{\circ}\). In \(\triangle SQR\), \(\angle SRQ=90^{\circ}\).

Step2: Check for common angles

\(\angle S\) is common to both \(\triangle STR\) and \(\triangle SQR\).

Step3: Apply AA (Angle - Angle) similarity criterion

Since two angles of \(\triangle STR\) (\(\angle S\) and \(\angle STR\)) are equal to two angles of \(\triangle SQR\) (\(\angle S\) and \(\angle SRQ\)), by AA similarity criterion \(\triangle STR\sim\triangle SQR\).

Answer:

\(\triangle STR\sim\triangle SQR\) (the third option)