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

B. of the AAS congruence theorem.

Explanation:

Triangles TSR and QRS share side SR

SR=RS

Angle TSR and Angle QRS are right angles, so

∠S= ∠R

Angle T Is-congruent-to Angle Q, so

∠T= ∠Q

From these data, we have one congruent side and two congruent angles. The possible congruence theorem that we can apply will be either ASA or AAS. In the ASA theorem, the congruence side must be between the two congruent angles.

The congruence side required for the ASA theorem for this triangle is ST = RQ. It is wrong because the congruent side we have is SR=RS. The correct option is the AAS theorem.