Question

given: ∠tsr and ∠qps are right angles; ∠t ≅ ∠q. prove: △tsr ≅ △qps. step 1: we know that ∠tsr ≅ ∠qps 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 ≅ △qps because of the asa congruence theorem. of the aas congruence theorem. of the third - angle theorem. all right triangles are congruent.

Explanation:

Step 1: Right angles congruent

∠TSR ≅ ∠QRS (all right angles congruent)

Step 2: Given angle congruence

∠T ≅ ∠Q (given)

Step 3: Reflexive property for side

$\overline{SR} \cong \overline{SR}$ (reflexive property)

Step 4: Apply AAS theorem

△TSR ≅ △QRS (two angles, non-included side congruent)

Answer:

of the AAS congruence theorem.