Congruent Triangle Proofs

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the significance of the term 'CPCTC' in triangle congruence?

Back

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

Front

What are the main criteria for proving triangle congruence?

Back

The main criteria for proving 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 SSS criterion state?

Back

The SSS criterion states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does the SAS criterion state?

Back

The SAS criterion states that 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 ASA criterion state?

Back

The ASA criterion states that 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 criterion state?

Back

The AAS criterion states that if two angles and a non-included side of one triangle are equal to two angles and a corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the HL criterion for triangle congruence?

Back

The HL criterion states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the significance of a bisector in triangle congruence?

Back

A bisector divides an angle or a side into two equal parts, which can help establish congruence between triangles by providing equal measures.

Front

What is the definition of corresponding parts in triangles?

Back

Corresponding parts in triangles refer to the sides and angles that are in the same relative position in two congruent triangles.