Use the image to answer the question.

Question

Two congruent triangles.

Investigate the patterns of the two triangles to determine which theorem proves that they are congruent.

(1 point)
Responses

SAS Theorem
SAS Theorem

SSS Theorem
SSS Theorem

HL Theorem
HL Theorem

ASA Theorem

Answer 1

To determine the congruence of two triangles, we can analyze the patterns and sides of the triangles involved.

1. SAS Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

2. SSS Theorem states that if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

3. HL Theorem applies specifically to right triangles, stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

4. ASA Theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Without the specific details from the image or the side/angle measurements, I cannot determine which theorem applies to your triangles. However, check the following:

• If you have two sides and the included angle equal, use SAS.
• If all three sides are equal, use SSS.
• If you are dealing with right triangles and know the hypotenuse and one leg, use HL.
• If you have two angles and the included side equal, use ASA.

Select the theorem that fits these criteria based on the properties of your triangles.