Question

find ps.
ps = \boxed{}

Explanation:

Step1: Identify Congruent Triangles

Triangles \( \triangle QPS \) and \( \triangle QRS \) are congruent (by AAS or HL, since \( \angle QPS = \angle QRS = 90^\circ \), \( \angle PQS=\angle RQS \), and \( QS \) is common). So corresponding sides \( PS \) and \( RS \) are equal.

Step2: Determine \( PS \)

Given \( RS = 12 \), so \( PS = RS = 12 \).

Answer:

\( 12 \)