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What are the 5 different theorems we will learn to prove triangles are congruent?

Hypotenuse Leg Theorem

Angle Side Angle Theorem

I do not know because I was not listening.



Side Side Side Theorem

Side Angle Side Theorem

Angle Angle Side Theorem

Submi

1 answer

In triangle congruence, there are several theorems that can be used to prove that two triangles are congruent. Here are five of the most commonly used theorems:

  1. Side Side Side (SSS) 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) 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) 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 theorem specifically applies to right triangles. It states that 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 for establishing triangle congruence based on different combinations of sides and angles.