Question

which similarity statement is true?
△srq ~ △qrt
△srq ~ △rts
△srq ~ △rtq
△srq ~ △trs

Explanation:

Step1: Recall the Right - Triangle Similarity Theorem

In a right - triangle, if an altitude is drawn from the right - angle vertex to the hypotenuse, then the two triangles formed are similar to the original triangle and to each other.

Step2: Analyze the given triangles

In \(\triangle SRQ\), \(\angle SRQ = 90^{\circ}\) (right - angle). \(RT\) is the altitude drawn to the hypotenuse \(SQ\).
By the Right - Triangle Similarity Theorem:

• \(\triangle SRQ\sim\triangle TRS\) (because \(\angle SRQ=\angle TRS = 90^{\circ}\) and \(\angle S\) is common to both \(\triangle SRQ\) and \(\triangle TRS\))
• \(\triangle SRQ\sim\triangle QRT\) (because \(\angle SRQ=\angle QRT = 90^{\circ}\) and \(\angle Q\) is common to both \(\triangle SRQ\) and \(\triangle QRT\))

Answer:

\(\triangle SRQ\sim\triangle TRS\)