Congruent Triangle Proofs

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What are the three main 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) - Note: SSA is NOT a congruence criterion.

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 is the definition of vertical angles?

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always congruent.

Front

What is the definition of alternate interior angles?

Back

Alternate interior angles are pairs of angles that are on opposite sides of a transversal and inside two parallel lines. They are congruent.

Front

What is the definition of alternate exterior angles?

Back

Alternate exterior angles are pairs of angles that are on opposite sides of a transversal and outside two parallel lines. They are congruent.

Front

What is the significance of a midpoint in triangle proofs?

Back

A midpoint divides a segment into two equal parts, which can be used to establish congruence in triangles.