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

Explanation:

Step1: Congruent right - angles

We have $\angle TSR\cong\angle QRS$ since all right angles are congruent.

Step2: Given congruent angles

$\angle T\cong\angle Q$ as given.

Step3: Reflexive property

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

Step4: Determine congruence theorem

We have two pairs of congruent angles ($\angle T\cong\angle Q$ and $\angle TSR\cong\angle QRS$) and a pair of congruent non - included sides. 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.