Triangle Congruence Proofs

Front

What is Triangle Congruence?

Back

Triangle congruence refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruence?

Back

The criteria for triangle congruence are: 1. Side-Side-Side (SSS) 2. Side-Angle-Side (SAS) 3. Angle-Side-Angle (ASA) 4. Angle-Angle-Side (AAS) 5. Hypotenuse-Leg (HL) for right triangles.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which is a criterion for triangle congruence stating 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 is a criterion for triangle congruence stating 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 is a criterion for triangle congruence stating 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 is a criterion for triangle congruence stating 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 triangle congruence applicable to right triangles, stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

Front

What is the definition of a bisector in geometry?

Back

A bisector is a line, ray, or segment that divides an angle or a segment into two equal parts.

Front

What is CPCTC in triangle proofs?

Back

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent', which is used to conclude that corresponding angles and sides of congruent triangles are equal.

Front

What is the Midpoint Theorem?

Back

The Midpoint Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long.