5.4 - CPCTC

Front

What does CPCTC stand for?

Back

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent.' It is a principle used in geometry to prove that if two triangles are congruent, then their corresponding sides and angles are also congruent.

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures, such as triangles, are congruent. It specifies which parts of the figures correspond to each other.

Front

How do you determine if two triangles are congruent?

Back

Two triangles can be determined to be congruent using several criteria: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

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Back

Front

What is the significance of corresponding sides in congruent triangles?

Back

In congruent triangles, corresponding sides are equal in length. This means that if two triangles are congruent, the lengths of their sides match up according to their congruence statement.

Front

What is the relationship between congruent triangles and their areas?

Back

Congruent triangles have the same area. Since they are identical in shape and size, the area calculated for one triangle will be the same for the other.

Front

How can you use CPCTC in a proof?

Back

CPCTC can be used in a proof to conclude that specific angles or sides are congruent after establishing that two triangles are congruent through one of the congruence criteria.

Front

What is the Angle-Angle (AA) criterion for triangle similarity?

Back

The Angle-Angle (AA) criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar, which implies that their corresponding sides are in proportion.

Front

What is the Side-Side-Side (SSS) criterion for triangle congruence?

Back

The Side-Side-Side (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 is the Side-Angle-Side (SAS) criterion for triangle congruence?

Back

The Side-Angle-Side (SAS) criterion states that if two sides of one triangle and the angle between them are equal to two sides of another triangle and the angle between them, then the triangles are congruent.