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

To determine which theorem proves that the two triangles are congruent, we need to examine the information given about the sides and angles of the triangles. Here’s a brief overview of the congruence theorems:

1. **SAS Theorem (Side-Angle-Side)**: Two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

2. **SSS Theorem (Side-Side-Side)**: Two triangles are congruent if all three sides of one triangle are equal to all three sides of another triangle.

3. **HL Theorem (Hypotenuse-Leg)**: This theorem applies specifically to right triangles and states that they are congruent if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle.

4. **ASA Theorem (Angle-Side-Angle)**: Two triangles are congruent if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle.

To choose the appropriate theorem, we need to identify which specific sides and angles are provided for the triangles in question. You should determine the configuration of the sides and angles you have before selecting the theorem that best matches the information.

If you want assistance in analyzing the specific attributes of your triangles, please provide more details.