Question

aors is a right triangle
select the correct similarity statement
△str ~ △tqr
△str ~ △rst
△str ~ △sqr
△str ~ △rtq

Explanation:

Step1: Recall the AA (Angle - Angle) similarity criterion

Two triangles are similar if two angles of one triangle are equal to two angles of another triangle.

Step2: Analyze \(\triangle STR\) and \(\triangle SQR\)

In right - triangle \(SQR\), \(\angle SRQ = 90^{\circ}\). Let's consider the angles. \(\angle S\) is common to both \(\triangle STR\) and \(\triangle SQR\). Also, \(\angle STR=\angle SRQ = 90^{\circ}\) (given \(T\) is a point such that \(RT\perp SQ\) in right - triangle \(SQR\)).
By the AA (Angle - Angle) similarity criterion, since two angles (\(\angle S\) and \(\angle STR=\angle SRQ\)) of \(\triangle STR\) are equal to two angles (\(\angle S\) and \(\angle SRQ\)) of \(\triangle SQR\), we can conclude that \(\triangle STR\sim\triangle SQR\)

Answer:

\(\triangle STR\sim\triangle SQR\)