Triangle Congruence Theorems

Front

What does the ASA theorem stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which states that 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 SSS theorem in triangle congruence?

Back

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

Front

Define the SAS theorem in triangle congruence.

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

What does the AAS theorem stand for?

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 a corresponding non-included side of another triangle, then the triangles are congruent.

Front

Explain the HL theorem in triangle congruence.

Back

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

Front

What is the AAA condition in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which states that if three angles of one triangle are equal to three angles of another triangle, the triangles are similar but not necessarily congruent.

Front

How can you prove triangles are congruent using the ASA theorem?

Back

To prove triangles are congruent using the ASA theorem, show that two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

What is the significance of the SSS theorem in triangle congruence?

Back

The SSS theorem is significant because it allows for the determination of triangle congruence based solely on the lengths of the sides, without needing to know any angles.

Front

When can the SAS theorem be applied?

Back

The SAS theorem can be applied when two sides and the included angle of one triangle are known and can be compared to two sides and the included angle of another triangle.

Front

What is the relationship between AAS and ASA theorems?

Back

AAS and ASA theorems are closely related; both can be used to prove triangle congruence, but AAS uses two angles and a non-included side, while ASA uses two angles and the included side.