Triangle Congruence

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

List the triangle congruence theorems.

Back

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

Front

What is the SSS Congruence Theorem?

Back

The SSS (Side-Side-Side) Congruence Theorem 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 Congruence Theorem?

Back

The SAS (Side-Angle-Side) Congruence Theorem 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 Congruence Theorem?

Back

The ASA (Angle-Side-Angle) Congruence Theorem 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 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 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 triangles are congruent.

Front

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

Back

AB ≅ XY, BC ≅ YZ, AC ≅ XZ.

Front

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

Back

All corresponding angles are equal.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size.