Question
What are the 5 different theorems we will learn to prove triangles are congruent? Angle Angle Side Theorem Side Angle Side Theorem Hypotenuse Leg Theorem Side Side Side Theorem Angle Side Angle Theorem I do not know because I was not listening.
Answers
GPT-4o mini
To prove triangles are congruent, there are several key theorems that you can learn. Here are the five different theorems you mentioned, along with a brief description of each:
1. **Side-Side-Side (SSS) Theorem**: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
2. **Side-Angle-Side (SAS) Theorem**: If two sides and the included angle (the angle between the two sides) 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) Theorem**: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
4. **Angle-Angle-Side (AAS) 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 applies specifically 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 two triangles are congruent.
These theorems are fundamental in geometry and help establish the congruence of triangles based on specific conditions related to their sides and angles.
1. **Side-Side-Side (SSS) Theorem**: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
2. **Side-Angle-Side (SAS) Theorem**: If two sides and the included angle (the angle between the two sides) 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) Theorem**: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
4. **Angle-Angle-Side (AAS) 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 applies specifically 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 two triangles are congruent.
These theorems are fundamental in geometry and help establish the congruence of triangles based on specific conditions related to their sides and angles.