3.5 Geometric Proofs 2 (CPCTC)

Front

What does CPCTC stand for in geometric proofs?

Back

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

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 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 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 two 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 two 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 two 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 the corresponding non-included side of another triangle, then the two triangles are congruent.

Front

What does the HL criterion state?

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 two triangles are congruent.

Front

How many given statements are needed in a proof using CPCTC?

Back

Three given statements are needed in a proof using CPCTC.

Front

What is the purpose of CPCTC in geometric proofs?

Back

The purpose of CPCTC in geometric proofs is to establish that corresponding parts of two congruent triangles are also congruent.