Intro to CONGRUENCE (CPCTC)

Front

What is congruence in geometry?

Back

Congruence in geometry means that two figures have the same shape and size. If two figures are congruent, they can be made to coincide by rigid motions such as translation, rotation, or reflection.

Front

What does CPCTC stand for?

Back

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

Front

If ΔABC ≅ ΔXYZ, what can we conclude about their corresponding angles?

Back

If ΔABC ≅ ΔXYZ, then ∠A ≅ ∠X, ∠B ≅ ∠Y, and ∠C ≅ ∠Z.

Front

What is the significance of the order of vertices in congruence?

Back

The order of vertices is significant because it indicates which angles and sides correspond to each other. For example, if ΔABC ≅ ΔDEF, then A corresponds to D, B corresponds to E, and C corresponds to F.

Front

If two triangles are congruent, what can we say about their sides?

Back

If two triangles are congruent, then their corresponding sides are equal in length.

Front

What is the SSS Congruence Postulate?

Back

The SSS (Side-Side-Side) Congruence Postulate 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 SAS Congruence Postulate?

Back

The SAS (Side-Angle-Side) Congruence Postulate 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 is the ASA Congruence Postulate?

Back

The ASA (Angle-Side-Angle) Congruence Postulate 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 is the AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence Theorem 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 is the HL Congruence Theorem?

Back

The HL (Hypotenuse-Leg) Congruence Theorem 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.