Question

given: \\( \angle tsr \\) and \\( \angle qrs \\) are right angles; \\( \angle t \cong \angle q \\) prove: \\( \triangle tsr \cong \triangle qrs \\) step 1: we know that \\( \angle tsr \cong \angle qrs \\) because all right angles are congruent. step 2: we know that \\( \angle t \cong \angle q \\) because it is given. step 3: we know that \\( \overline{sr} \cong \overline{rs} \\) because of the reflexive property. step 4: \\( \triangle tsr \cong \triangle qrs \\) because all right triangles are congruent. of the third angle theorem. of the aas congruence theorem. of the asa congruence theorem.

Explanation:

Step1: Analyze the given information

We have two angles ($\angle TSR\cong\angle QRS$, $\angle T\cong\angle Q$) and a non - included side ($\overline{SR}\cong\overline{RS}$).

Step2: Recall congruence theorems

The AAS (Angle - Angle - Side) congruence theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Answer:

of the AAS congruence theorem.