Question

Which theorem proves the two triangles are congruent?

HL

SAS

AAS
SSS
ASA
the triangles are not congruent

Answer 1

The theorem used to prove that two triangles are congruent depends on the specific conditions you have for the triangles. Here are the meanings of the congruence conditions you've listed:

1. **HL (Hypotenuse-Leg)**: This theorem applies specifically to right triangles. If the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

2. **SAS (Side-Angle-Side)**: If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, then the triangles are congruent.

3. **AAS (Angle-Angle-Side)**: If two angles and a non-included side of one triangle are equal to the corresponding two angles and the non-included side of another triangle, then the triangles are congruent.

4. **SSS (Side-Side-Side)**: If all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

5. **ASA (Angle-Side-Angle)**: If two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle, then the triangles are congruent.

6. **The triangles are not congruent**: This would be the conclusion if none of the conditions above are met.

To determine which theorem applies, you need to analyze the information you have about the triangles. If you provide specific details about the sides or angles of the triangles in question, I can help you determine the correct theorem for proving their congruence.