Triangle Congruence Statements

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 all corresponding sides and angles are equal.

Front

What are the congruence statements for triangles?

Back

Congruence statements indicate that two triangles are congruent, typically written as △ABC ≅ △DEF, where corresponding vertices are matched.

Front

What is the significance of corresponding sides and angles in triangle congruence?

Back

If two triangles are congruent, their corresponding sides and angles are also congruent, meaning they have equal lengths and measures.

Front

What is the SSS (Side-Side-Side) Congruence Postulate?

Back

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

Front

What is the SAS (Side-Angle-Side) Congruence Postulate?

Back

The SAS 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 triangles are congruent.

Front

What is the ASA (Angle-Side-Angle) Congruence Postulate?

Back

The ASA 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 triangles are congruent.

Front

What is the AAS (Angle-Angle-Side) Congruence Theorem?

Back

The AAS 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 triangles are congruent.

Front

What is the HL (Hypotenuse-Leg) Congruence Theorem?

Back

The HL 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 triangles are congruent.

Front

How do you write a congruence statement for triangles?

Back

To write a congruence statement, match the corresponding vertices of the triangles, such as △ABC ≅ △DEF, where A corresponds to D, B to E, and C to F.

Front

What is the relationship between the angles and sides of congruent triangles?

Back

In congruent triangles, corresponding angles are equal, and corresponding sides are proportional.