Question
Which theorem proves the two triangles are congruent?
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GPT-4o mini
To determine whether two triangles are congruent, there are several theorems that can be applied. The most common ones are:
1. **Side-Side-Side (SSS) Congruence Theorem**: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
2. **Side-Angle-Side (SAS) Congruence Theorem**: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
3. **Angle-Side-Angle (ASA) Congruence Theorem**: 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 two triangles are congruent.
4. **Angle-Angle-Side (AAS) Congruence Theorem**: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
5. **Hypotenuse-Leg (HL) Theorem**: This is a special case for 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 two triangles are congruent.
You would choose the appropriate theorem based on the information available about the triangles.
1. **Side-Side-Side (SSS) Congruence Theorem**: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
2. **Side-Angle-Side (SAS) Congruence Theorem**: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
3. **Angle-Side-Angle (ASA) Congruence Theorem**: 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 two triangles are congruent.
4. **Angle-Angle-Side (AAS) Congruence Theorem**: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
5. **Hypotenuse-Leg (HL) Theorem**: This is a special case for 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 two triangles are congruent.
You would choose the appropriate theorem based on the information available about the triangles.
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