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 difference between ASA and AAS?

Back

The main difference is that ASA includes the side between the two angles, while AAS includes a side that is not between the two angles.

Front

Can two triangles be congruent if only two angles are known?

Back

No, two triangles cannot be proven congruent with only two angles known; a third side or angle must also be known.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

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 the included side in ASA?

Back

The included side in ASA is the side that is between the two angles; it is crucial for establishing congruence.

Front

What theorem can be used if two angles and a non-included side are known?

Back

The AAS theorem can be used if two angles and a non-included side are known to prove triangle congruence.

Front

What does it mean if two triangles are not congruent?

Back

If two triangles are not congruent, it means that at least one pair of corresponding sides or angles is not equal.

Front

What is an example of a situation where AAS can be applied?

Back

If triangle ABC has angles A and B equal to angles D and E in triangle DEF, and side AC equal to side DF, then triangles ABC and DEF are congruent by AAS.