Two congruent triangles.

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

ASA Theorem
ASA Theorem

HL Theorem

Answer 1

To determine which theorem proves that two congruent triangles are indeed congruent, we need to analyze the characteristics of the triangles.

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

2. SAS Theorem (Side-Angle-Side): If two sides of one triangle are congruent to two sides of another triangle and the angle between those sides is congruent, then the triangles are congruent.

3. ASA Theorem (Angle-Side-Angle): If two angles and the side between them of one triangle are congruent to two angles and the side between them of another triangle, then the triangles are congruent.

4. HL Theorem (Hypotenuse-Leg): This is specific 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, then the triangles are congruent.

To provide an accurate response, you would need to identify the specific congruence relationships in your two triangles. If you have measurements or properties that indicate the triangles are congruent based on any of the above criteria, then you would select the corresponding theorem.

Since no specific information about the triangles is provided here, you can consider the conditions mentioned above to choose the right theorem. If you determine that all three sides are equal, then you'd say SSS Theorem. If two sides and the included angle are equal, then you would state SAS Theorem, and so on for ASA and HL.