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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

Please help Given: ∠TRS = ∠URS ∠TSR = ∠USR Based on the given information and the-example-1

2 Answers

7 votes
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.
User Sarena
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8.4k points
5 votes

Answer:

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

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 .

User Reorx
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8.5k points