Congruent Triangles Practice

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 AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a postulate that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-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 is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, often written in the form of '∆ABC ≅ ∆XYZ'.

Front

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

Back

If ∆ABC ≅ ∆XYZ, then corresponding sides and angles are congruent: AB ≅ XY, BC ≅ YZ, AC ≅ XZ and ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles are significant because they allow us to establish that two shapes are identical in size and shape, which is essential for solving many geometric problems.

Front

What is the difference between congruence and similarity?

Back

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

Front

How can you prove that two triangles are congruent?

Back

You can prove that two triangles are congruent using postulates such as ASA, AAS, SAS, or by showing that all corresponding sides and angles are congruent.

Front

What is the Angle-Angle (AA) criterion for triangle similarity?

Back

The AA criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Front

What is the Side-Side-Side (SSS) criterion for triangle congruence?

Back

The SSS criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.