Question

u is the midpoint of \\( \overline{qs} \\), \\( \overline{qt} \perp \overline{qs} \\), and \\( \overline{qs} \perp \overline{rs} \\). complete the proof that \\( \triangle rsu \cong \triangle tqu \\).

Explanation:

Step1: Identify reason for Step6

Vertical angles are congruent. So $\angle QUT \cong \angle RUS$ because they are vertical angles.

Step2: Identify reason for Step7

We have two angles and the included side congruent: $\angle Q \cong \angle S$, $\overline{QU} \cong \overline{SU}$, $\angle QUT \cong \angle RUS$. This is ASA congruence.

Answer:

Step6 Reason: Vertical angles are congruent
Step7 Reason: ASA Congruence Criterion
$\triangle RSU \cong \triangle TQU$