Question

given: ∠tsr and ∠qrs are right angles; ∠t≅∠q
prove: △tsr≅△qrs
t s
r q
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

$\angle TSR\cong\angle QRS$ (all right angles are congruent)

Step2: Given angle congruence

$\angle T\cong\angle Q$ (given)

Step3: Reflexive property of side

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

Step4: Identify congruence theorem

We have two pairs of angles and a non - included side. By the AAS (Angle - Angle - Side) congruence theorem, $\triangle TSR\cong\triangle QRS$.

Answer:

of the AAS congruence theorem.