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

Answer: AAS

Explanation:

We can think of side SR as the side opposite angle Q.

So in triangle QRS, we have angle Q, the side opposite angle Q, and and angle R.

This is obviously a case of AAS congruency.