Triangle Congruence Statements

Front

What is a triangle congruence statement?

Back

A triangle congruence statement indicates that two triangles are congruent, meaning they have the same size and shape, and their corresponding sides and angles are equal.

Front

What does the symbol '≅' represent in geometry?

Back

The symbol '≅' represents congruence, indicating that two geometric figures are congruent.

Front

List the criteria for triangle congruence.

Back

1. Side-Side-Side (SSS) Congruence 2. Side-Angle-Side (SAS) Congruence 3. Angle-Side-Angle (ASA) Congruence 4. Angle-Angle-Side (AAS) Congruence 5. Hypotenuse-Leg (HL) Congruence (for right triangles)

Front

If ∆ABC ≅ ∆XYZ, what can we conclude about their corresponding sides?

Back

AB ≅ XY, BC ≅ YZ, AC ≅ XZ.

Front

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

Back

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Front

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

Back

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

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

Back

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Front

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

Back

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Front

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

Back

In right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, then the two triangles are congruent.

Front

How do you denote the congruence of triangles in a statement?

Back

By writing the triangle names with the corresponding vertices in the same order, e.g., ∆ABC ≅ ∆XYZ.