Congruent Triangles

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a postulate that states if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a postulate that states if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Front

If ∆ABC≅∆XYZ, what can be concluded about the sides AB and XY?

Back

If ∆ABC≅∆XYZ, then AB is congruent to XY (AB≅XY).

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the Angle-Angle (AA) similarity postulate?

Back

The AA similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar, but not necessarily congruent.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that triangles are identical in size and shape, while similarity means that triangles have the same shape but may differ in size.

Front

How can you prove that two triangles are congruent using the SAS postulate?

Back

To prove triangles are congruent using SAS, show that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Front

What is the significance of the included angle in the SAS postulate?

Back

The included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence in the SAS postulate.

Front

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

Back

No, knowing only one side is not sufficient to prove congruence; at least two sides and the included angle (SAS) or other congruence criteria must be used.