Triangle Congruence Proofs

Front

What is Triangle Congruence?

Back

Triangle congruence means that two triangles are identical in shape and size, which can be proven using various criteria.

Front

List the criteria for triangle congruence.

Back

1. SSS (Side-Side-Side) 2. SAS (Side-Angle-Side) 3. ASA (Angle-Side-Angle) 4. AAS (Angle-Angle-Side) 5. HL (Hypotenuse-Leg for right triangles)

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which states that 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 states that 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 states that 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 states that 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, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, which is a criterion for proving the congruence of right triangles based on the equality of the hypotenuse and one leg.

Front

What is the Vertical Angle Theorem?

Back

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

Front

What is the Reflexive Property?

Back

The Reflexive Property states that any geometric figure is congruent to itself, which is often used in proofs.

Front

What are Alternate Interior Angles?

Back

Alternate interior angles are pairs of angles that are on opposite sides of a transversal and inside the two lines. If the lines are parallel, these angles are congruent.