Triangle Congruence Proofs

Front

What is the definition of congruence in geometry?

Back

Congruence in geometry means that two figures have the same shape and size, and can be made to coincide by rigid transformations such as translation, rotation, or reflection.

Front

What does the Angle Bisector Theorem state?

Back

The Angle Bisector Theorem states that the angle bisector of an angle in a triangle divides the opposite side into two segments that are proportional to the lengths of the other two sides.

Front

What is the Reflexive Property?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning that for any triangle ABC, triangle ABC is congruent to triangle ABC.

Front

What does the Vertical Angle Theorem state?

Back

The Vertical Angle Theorem states that when two lines intersect, the opposite (or vertical) angles are congruent.

Front

What is the SSS Congruence Postulate?

Back

The SSS (Side-Side-Side) Congruence Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Front

What is the SAS Congruence Postulate?

Back

The SAS (Side-Angle-Side) Congruence Postulate states that 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.

Front

What is the ASA Congruence Postulate?

Back

The ASA (Angle-Side-Angle) Congruence Postulate states that 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.

Front

What is the AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence Theorem states that 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.

Front

What is the HL Congruence Theorem?

Back

The HL (Hypotenuse-Leg) Congruence Theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

How can you determine if two triangles are congruent using the AAS method?

Back

To determine if two triangles are congruent using the AAS method, check if two angles and a non-included side of one triangle are congruent to the corresponding two angles and the non-included side of the other triangle.