Question

Given: Angle T S R and Angle Q R S are right angles; Angle T Is-congruent-to Angle Q
Prove: Triangle T S R Is-congruent-to Triangle Q R S

Triangles T S R and Q R S share side S R. Angles T S R and S R Q are right angles. Angles S T R and S Q R are congruent.

Step 1: We know that Angle T S R Is-congruent-to Angle Q R S because all right angles are congruent.
Step 2: We know that Angle T Is-congruent-to Angle Q because it is given.
Step 3: We know that Line segment S R is-congruent-to line segment R S because of the reflexive property.
Step 4: Triangle T S R Is-congruent-to Triangle Q R S because

of the ASA congruence theorem.
of the AAS congruence theorem.
of the third angle theorem.
all right triangles are congruent.

Answer 1

Step 4: of the AAS congruence theorem.

Reason: We have two pairs of congruent angles (∠TSR ≅ ∠QRS, both right angles, and ∠STR ≅ ∠SQR given) and the non‑included side SR ≅ RS (reflexive). Two angles and a non‑included side give triangle congruence by AAS.