Triangle Congruence Theorems

Front

What is the SAS (Side-Angle-Side) Congruence Theorem?

Back

The SAS Congruence Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle between those sides is also congruent, then the two triangles are congruent.

Front

What is the AAS (Angle-Angle-Side) Congruence Theorem?

Back

The AAS Congruence Theorem states that if two angles and the 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.

Front

What is the ASA (Angle-Side-Angle) Congruence Theorem?

Back

The ASA Congruence Theorem states that if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the two triangles are congruent.

Front

What is the HL (Hypotenuse-Leg) Congruence Theorem?

Back

The HL Congruence Theorem applies to right triangles and 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.

Front

What is the AAA (Angle-Angle-Angle) condition?

Back

The AAA condition states that if three angles of one triangle are congruent to three angles of another triangle, the triangles are similar but not necessarily congruent.

Front

What additional information is needed to prove triangles are congruent by SAS?

Back

You need to show that the included angle between the two sides is congruent.

Front

What additional information is needed to prove triangles are congruent by AAS?

Back

You need to show that one of the angles is congruent to the corresponding angle in the other triangle.

Front

How do you denote congruent segments?

Back

Front

How do you denote congruent angles?

Back

Front

What is the significance of the included angle in triangle congruence?

Back

The included angle is crucial in the SAS and ASA theorems as it helps establish the congruence of the triangles based on the sides and angles provided.