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} cong overline{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: Identify congruent angles

$\angle TSR \cong \angle QRS$ (right angles)
$\angle T \cong \angle Q$ (given)

Step2: Identify congruent side

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

Step3: Match to congruence rule

We have two pairs of congruent angles and a non-included congruent side, which fits AAS.

Answer:

of the AAS congruence theorem.