ASA and AAS △ Congruence

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem that states 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 does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states 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 ASA Congruence Theorem?

Back

The ASA Congruence Theorem states that if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the two triangles are congruent.

Front

What is the AAS Congruence Theorem?

Back

The AAS Congruence Theorem states that if two angles and a side not between them in one triangle are equal to two angles and the corresponding side in another triangle, then the two triangles are congruent.

Front

Can two triangles be congruent if only one angle and one side are known?

Back

No, two triangles cannot be proven congruent with only one angle and one side. More information is needed, such as another angle or side.

Front

What is the difference between ASA and AAS?

Back

The difference is that ASA requires the side to be between the two angles, while AAS does not require the side to be between the two angles.

Front

If two triangles have two pairs of equal angles, what can be concluded?

Back

If two triangles have two pairs of equal angles, they are congruent by the AAS theorem.

Front

What is the significance of congruent triangles in geometry?

Back

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

Front

What is the definition of congruence in geometry?

Back

Congruence in geometry means that two figures have the same shape and size, allowing them to be superimposed on each other.

Front

What is an example of using ASA to prove triangle congruence?

Back

If triangle ABC has angles A and B equal to angles D and E in triangle DEF, and side AB is equal to side DE, then triangle ABC is congruent to triangle DEF by ASA.