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 a 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 you prove triangles congruent using ASA?

Back

Yes, if you know two angles and the included side of one triangle are equal to two angles and the included side of another triangle, you can prove the triangles are congruent using the ASA theorem.

Front

Can you prove triangles congruent using AAS?

Back

Yes, if you know two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, you can prove the triangles are congruent using the AAS theorem.

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 allows the side to be outside the two angles.

Front

If two triangles have two equal angles, what can be said about their sides?

Back

If two triangles have two equal angles, the sides opposite those angles are proportional, but the triangles may not be congruent unless a third side is also known.

Front

What is the importance of congruence in triangles?

Back

Congruence in triangles is important because it allows us to conclude that the triangles are identical in shape and size, which is useful in various applications in geometry.

Front

How can you identify congruent triangles using ASA?

Back

To identify congruent triangles using ASA, check if two angles and the included side of one triangle match with two angles and the included side of another triangle.