Triangle Congruence Theorems

Front

What is the definition of congruence in geometry?

Back

Two figures are congruent if they have the same shape and size, meaning one can be transformed into the other through rotations, translations, or reflections.

Front

What does the SAS (Side-Angle-Side) 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 triangles are congruent.

Front

What does the SSS (Side-Side-Side) theorem state?

Back

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

Front

What does the ASA (Angle-Side-Angle) 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 triangles are congruent.

Front

What does the AAS (Angle-Angle-Side) 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 triangles are congruent.

Front

What does the HL (Hypotenuse-Leg) 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 triangles are congruent.

Front

What is the definition of vertical angles?

Back

Vertical angles are the angles opposite each other when two lines cross. They are always equal.

Front

What is the Reflexive Property?

Back

The Reflexive Property states that any geometric figure is congruent to itself.

Front

What is the definition of a midpoint?

Back

A midpoint is a point that divides a line segment into two equal parts.

Front

What is the Vertical Angle Theorem?

Back

The Vertical Angle Theorem states that vertical angles are congruent.