Triangle Congruence Proofs

Front

What is Triangle Congruence?

Back

Triangle Congruence refers to the condition where two triangles are considered congruent if their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruence?

Back

The criteria for triangle congruence are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Front

What does the Reflexive Property state?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning AB ≅ AB.

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 Angles Theorem?

Back

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

Front

What is the definition of an angle bisector?

Back

An angle bisector is a ray that divides an angle into two equal angles.

Front

What does it mean for two angles to be complementary?

Back

Two angles are complementary if the sum of their measures is 90 degrees.

Front

What does it mean for two angles to be supplementary?

Back

Two angles are supplementary if the sum of their measures is 180 degrees.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the significance of the Hypotenuse-Leg (HL) theorem?

Back

The HL theorem states that 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.