Question

16,905 Learners found this answer helpful

what is rs?
rs =
submit

Explanation:

Step1: Identify Congruent Triangles

Triangles \( \triangle QPS \) and \( \triangle QRS \) have: \( \angle QPS = \angle QRS = 90^\circ \), \( \angle PQS = \angle RQS = 61^\circ \), and \( QS \) is common. By AAS (Angle - Angle - Side) congruence, \( \triangle QPS \cong \triangle QRS \).

Step2: Corresponding Parts of Congruent Triangles

In congruent triangles, corresponding sides are equal. Since \( PS = 12 \) (given) and \( PS \) corresponds to \( RS \) in \( \triangle QPS \) and \( \triangle QRS \) respectively, we have \( RS = PS \).

Answer:

\( 12 \)