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 (overline{sr}congoverline{rs}) because of the reflexive property. step 4: △tsr≅△qrs because of the third - angle theorem. of the asa congruence theorem. all right triangles are congruent. of the aas congruence theorem.

Explanation:

Step1: Identify congruent angles

We have $\angle TSR\cong\angle QRS$ (right - angle congruence) and $\angle T\cong\angle Q$ (given).

Step2: Identify congruent side

$\overline{SR}\cong\overline{RS}$ by reflexive property.

Step3: Apply congruence theorem

We have two pairs of congruent 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.