Chapter 5 - Triangle Congruence Theorems

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, if triangle ABC is considered, then triangle ABC ≅ triangle ABC.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle. It is a theorem 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. It is a theorem 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. It is a theorem 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. It is a theorem that states if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What is the definition of congruence in geometry?

Back

Congruence in geometry means that two figures have the same shape and size. Congruent figures can be superimposed on each other.

Front

What is the significance of vertical angles in triangle congruence?

Back

Vertical angles are always congruent. This property can be used in proofs to establish congruence between triangles.

Front

How can you prove triangles are congruent using the ASA theorem?

Back

To prove triangles are congruent using the ASA theorem, you need to show that two angles and the side between them in one triangle are congruent to the corresponding two angles and the side in another triangle.

Front

How can you prove triangles are congruent using the AAS theorem?

Back

To prove triangles are congruent using the AAS theorem, you need to show that two angles and a non-included side in one triangle are congruent to the corresponding two angles and the non-included side in another triangle.

Front

How can you prove triangles are congruent using the SAS theorem?

Back

To prove triangles are congruent using the SAS theorem, you need to show that two sides and the included angle in one triangle are congruent to the corresponding two sides and the included angle in another triangle.