Triangle Congruence Theorems

Front

What are congruent figures?

Back

Congruent figures have the same dimensions (side lengths and angle measures), are the same shape and size, and can be mapped onto one another using rigid motions.

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What does SAS stand for in triangle congruence?

Back

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

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which means if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which means 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, the triangles are congruent.

Front

What is the Reflexive Property of Equality (POE)?

Back

The Reflexive Property states that a side or angle is congruent to itself.

Front

What is the Transitive Property of Equality (POE)?

Back

The Transitive Property states that if one figure is congruent to a second figure, and the second figure is congruent to a third figure, then the first figure is congruent to the third figure.

Front

What is the definition of vertical angles?

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always congruent.

Front

How can you determine if two triangles are congruent?

Back

You can determine if two triangles are congruent by using the SSS, SAS, ASA, or AAS congruence theorems.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle formed between the two sides being compared, and it is crucial for establishing congruence.