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

What is the ASA congruence criterion?

Back

The ASA (Angle-Side-Angle) criterion 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 criterion?

Back

The AAS (Angle-Angle-Side) criterion 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 SAS congruence criterion?

Back

The SAS (Side-Angle-Side) criterion 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 SSS congruence criterion?

Back

The SSS (Side-Side-Side) criterion states that if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What is the AAA condition in triangle congruence?

Back

The AAA (Angle-Angle-Angle) condition states that if two triangles have equal corresponding angles, they are similar but not necessarily congruent.

Front

If ∠A ≅ ∠D, what can we say about triangles that include these angles?

Back

If ∠A ≅ ∠D and the triangles have other congruent sides or angles, we can use congruence criteria to determine if the triangles are congruent.

Front

What is the significance of the included angle in triangle congruence?

Back

The included angle is the angle formed between two sides of a triangle. It is crucial in the SAS and ASA criteria for proving triangle congruence.

Front

Can two triangles be congruent if only one side is known to be equal?

Back

No, knowing only one side is not sufficient to prove congruence. At least two sides and the included angle or two angles and the included side must be known.

Front

What does the term 'corresponding parts' refer to in triangle congruence?

Back

Corresponding parts refer to the sides and angles of two triangles that are equal when the triangles are congruent.