Congruent Triangles

Front

What are congruent triangles?

Back

Triangles that have the same size and shape, meaning all corresponding sides and angles are equal.

Front

What does the AAS postulate stand for?

Back

Angle-Angle-Side postulate, which 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 does the SAS postulate stand for?

Back

Side-Angle-Side postulate, which 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 does the ASA postulate stand for?

Back

Angle-Side-Angle postulate, which states that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Front

What does the SSS postulate stand for?

Back

Side-Side-Side postulate, which 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 significance of the SSA condition in triangle congruence?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

If ∆ABC≅∆XYZ, what can we conclude about the sides AB and XY?

Back

AB≅XY, meaning side AB of triangle ABC is equal in length to side XY of triangle XYZ.

Front

What information is needed to prove triangles congruent using ASA?

Back

Two angles and the included side must be known.

Front

What is the relationship between corresponding angles in congruent triangles?

Back

Corresponding angles in congruent triangles are equal.

Front

What is the relationship between corresponding sides in congruent triangles?

Back

Corresponding sides in congruent triangles are equal in length.