Question

please help
Given:
∠TRS = ∠URS
∠TSR = ∠USR

Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove the triangles congruent. If it is not possible to prove the triangles are congruent, choose "not possible".

SSS
SAS
ASA
not possible

Answer 1

The given info gives you two pairs of congruent angles.
Side RS is the included side. It is a side of both triangles, and it is congruent to itself. Since you now have side RS congruent to side RS, you can use ASA.

Answer 2

Answer:

ASA  is a possible  congruent theorem that could be used to prove the triangles congruent.

Step-by-step explanation:

Given

$\angle TRS=\angle URS$

$\angle TSR=\angle USR$

Proof: In triangle STR and SUR

1.Statement: $\angle TSR=\angle USR$

Reason: Given

2.Statement: $\angle TRS= \angle URS$

Reason: Given

3.Statement: RS=RS

Reason: Reflexive property of equality.

4.Statement: $\triangle STR \cong \triangle SUR$

Reason: ASA ( Angle-Side-Angle) property of congruence.

Hence, the triangle are congruent by the ASA congruence theorem .