Answer:
The answer is number (2) ⇒ because of the AAS congruence theorem
Step-by-step explanation:
* Lets use the information to solve the problem
- In the given triangles TSR and QRS
# We have a common side RS or SR
# Two right angles TSR and QRS
# m∠T = m∠Q ⇒ given
* So we have two pairs of angles and one common side, lets
revise the cases of congruence
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and
including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ
≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles
and one side in the 2ndΔ
* Now lets read the statements and write the missing
Step 1: m∠TSR = m∠QRS = 90° ⇒ because all right angles are congruent
Step 2: m∠T = m∠Q ⇒ because it is given
Step 3: SR ≅ RS ⇒ because of reflexive property (common side)
Step 4: Δ TSR ≅ ΔQRS ⇒ because of the AAS congruence theorem
* The answer is number (2)
