Use the image to answer the question. Investigate the patterns of the two triangles to determine which theorem proves that they are congruent. (1 point) Responses SSS Theorem SSS Theorem SAS Theorem SAS Theorem HL Theorem HL Theorem ASA Theorem

Answer 1

To determine the congruence of the two triangles based on the provided options, we need to analyze the information:

• SSS Theorem (Side-Side-Side): This theorem states that if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

• SAS Theorem (Side-Angle-Side): This theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the angles between those sides are congruent, then the triangles are congruent.

• ASA Theorem (Angle-Side-Angle): This theorem states that if two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent.

• HL Theorem (Hypotenuse-Leg): This theorem applies specifically to right triangles. It states that if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, then the triangles are congruent.

To choose the correct theorem without the visual of the triangles, you would need to know:

1. Whether the triangles have congruent corresponding sides or angles.
2. Whether they are right triangles or not.

Without the visual, based on typical scenarios, if both triangles either show three pairs of equal corresponding sides, then SSS would apply. If two sides and the angle between them are shown to be equal, SAS would apply. If two angles and the side between them are shown to be equal, ASA would apply. If they are right triangles with the hypotenuse and one leg equal, HL would apply.

Please check the image or description of the triangles to identify which of these criteria fit, and based on that, select the appropriate theorem.