Triangle Congruence Theorems

Front

What is the definition of congruence in triangles?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

What does the SSS (Side-Side-Side) Congruence Theorem state?

Back

If three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What does the SAS (Side-Angle-Side) Congruence Theorem state?

Back

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What does the ASA (Angle-Side-Angle) Congruence Theorem state?

Back

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What does the AAS (Angle-Angle-Side) Congruence Theorem state?

Back

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 two triangles are congruent.

Front

What does the HL (Hypotenuse-Leg) Congruence Theorem state?

Back

In right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the two triangles are congruent.

Front

What is the Vertical Angle Theorem?

Back

Vertical angles are congruent, meaning if two angles are opposite each other when two lines intersect, they are equal in measure.

Front

What is the Reflexive Property of Congruence?

Back

Front

What is the definition of corresponding parts in congruent triangles?

Back

Corresponding parts are the sides and angles of two triangles that are equal in measure when the triangles are congruent.

Front

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

Back

Measure all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.