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 of the asa congruence theorem. of the asa congruence theorem. of the aas congruence theorem. of the third angle theorem. all right triangles are congruent.

Explanation:

Step1: Identify congruent angles and sides

We know that \(\angle TSR\cong\angle QRS\) (right angles), \(\angle T\cong\angle Q\) (given), and \(\overline{SR}\cong\overline{RS}\) (reflexive property).

Step2: Apply congruence theorem

We have two angles and a non - included side (AAS - Angle - Angle - Side) congruent.

Answer:

of the AAS congruence theorem.