ASA and AAS △ Congruence

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence.

Front

What is the ASA Congruence Theorem?

Back

The ASA Congruence Theorem states that 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 is the AAS Congruence Theorem?

Back

The AAS Congruence Theorem states that 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

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

Back

No, at least two angles and one side (ASA or AAS) are needed to prove congruence.

Front

What is the difference between ASA and AAS?

Back

ASA requires the included side between the two angles, while AAS does not require the side to be included between the two angles.

Front

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

Back

The triangles are congruent by the AAS theorem.

Front

If two triangles have two pairs of equal sides and the included angle, what can be concluded?

Back

The triangles are congruent by the ASA theorem.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which allows for the transfer of properties and measurements.

Front

Can the AAS theorem be used if the side is between the two angles?

Back

Yes, if the side is between the two angles, it can also be used with ASA.