CPCTC Congruent Triangles

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Front

If two triangles are congruent, what can be said about their corresponding angles?

Back

If two triangles are congruent, their corresponding angles are also congruent.

Front

If ∆XYZ ≅ ∆KLM, what can be concluded about the sides of the triangles?

Back

If ∆XYZ ≅ ∆KLM, then the corresponding sides are also congruent, meaning \overline{XY} \cong \overline{KL}, \overline{YZ} \cong \overline{LM}, and \overline{ZX} \cong \overline{MK}.

Front

What is the significance of the congruence symbol (≅) in geometry?

Back

The congruence symbol (≅) indicates that two geometric figures, such as triangles, are congruent, meaning they have the same shape and size.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have exactly the same size and shape, with corresponding sides and angles that are equal.

Front

What is the relationship between the angles of congruent triangles?

Back

The angles of congruent triangles are equal; if two triangles are congruent, then each angle in one triangle is equal to the corresponding angle in the other triangle.

Front

What is the purpose of the CPCTC theorem in triangle congruence?

Back

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent, which states that if two triangles are proven to be congruent, then all their corresponding parts (sides and angles) are also congruent.

Front

How can you prove that two triangles are congruent using the SSS criterion?

Back

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

Front

What is the difference between AAS and ASA in triangle congruence?

Back

AAS (Angle-Angle-Side) involves two angles and a non-included side, while ASA (Angle-Side-Angle) involves two angles and the included side between them.