Question

given: ∠tsr and ∠qrs are right angles; ∠t ≅ ∠q. prove: △tsr ≅ △qrs. step 1: we know that ∠tsr ≅ ∠qrs because all right angles are congruent. step 2: we know that ∠t ≅ ∠q because it is given. step 3: we know that sr ≅ rs because of the reflexive property. step 4: △tsr ≅ △qrs because of the asa congruence theorem. of the aas congruence theorem. of the third angle theorem. all right triangles are congruent.

Explanation:

Step1: Establish right - angle congruence

All right angles are congruent, so $\angle TSR\cong\angle QRS$.

Step2: Acknowledge given angle congruence

It is given that $\angle T\cong\angle Q$.

Step3: Identify reflexive - property side congruence

By the reflexive property, $\overline{SR}\cong\overline{RS}$.

Step4: Determine congruence theorem

We have two pairs of angles and a non - included side congruent. 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.