Triangle Congruence Statements

Front

What is a triangle congruence statement?

Back

A triangle congruence statement is a mathematical assertion that two triangles are congruent, meaning they have the same size and shape. This is often denoted as ∆ABC ≅ ∆DEF.

Front

What does the symbol '≅' represent in geometry?

Back

The symbol '≅' represents congruence, indicating that two geometric figures are identical in shape and size.

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 ≅ ∆DEF, what can we conclude about their corresponding angles?

Back

The corresponding angles of the triangles are congruent, meaning ∠A ≅ ∠D, ∠B ≅ ∠E, and ∠C ≅ ∠F.

Front

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

Back

The corresponding sides of the triangles are equal in length, meaning AB = DE, BC = EF, and AC = DF.

Front

What is the Side-Side-Side (SSS) 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 two triangles are congruent.

Front

What is the Side-Angle-Side (SAS) 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 two triangles are congruent.

Front

What is the Angle-Side-Angle (ASA) 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 two triangles are congruent.

Front

What is the Angle-Angle-Side (AAS) 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 two triangles are congruent.

Front

What is the Hypotenuse-Leg (HL) 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 two triangles are congruent.