Question

Which triangle congruence criterion would you use to state that the given triangles are congruent?

(1 point)
Responses

SAS
SAS

AAS
AAS

HL
HL

SSS

Answer 1

To determine which triangle congruence criterion applies, you need to analyze the information given about the triangles. Here are the criteria:

1. **SAS (Side-Angle-Side)**: This criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

2. **AAS (Angle-Angle-Side)**: This criterion states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

3. **HL (Hypotenuse-Leg)**: This criterion applies specifically to right triangles. If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, they are congruent.

4. **SSS (Side-Side-Side)**: This criterion states that if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Without specific information about the triangles in question, it's not possible to decisively select a criterion. However, you would typically choose based on the information presented in your problem:

- If you have two sides and the angle between them, use **SAS**.
- If you have two angles and a side (not between them), use **AAS**.
- If both triangles are right triangles and you know the hypotenuse and one leg, use **HL**.
- If you know all three sides of both triangles, use **SSS**.

Please provide more specific details about the triangles for a more precise selection of the appropriate congruence criterion.