Triangle Congruence Theorems

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a postulate that states if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What is the SAS postulate?

Back

SAS stands for Side-Angle-Side, which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

Define the SSS postulate.

Back

SSS stands for Side-Side-Side, which states that if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the HL theorem?

Back

HL stands for Hypotenuse-Leg, which is a theorem used to prove the congruence of right triangles. It states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

How can you prove triangles are congruent using SAS?

Back

To prove triangles are congruent using SAS, show that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What is the difference between ASA and AAS?

Back

ASA requires the included side between two angles to be equal, while AAS allows for a non-included side to be equal.

Front

When can you use the SSS postulate?

Back

You can use the SSS postulate when you know all three sides of one triangle are equal to all three sides of another triangle.

Front

What is the significance of the HL theorem?

Back

The HL theorem is significant because it provides a method to prove the congruence of right triangles, which is a specific case of triangle congruence.

Front

How do you identify congruent triangles using AAS?

Back

To identify congruent triangles using AAS, show that two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.