ASA and AAS △ Congruence

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem used to prove that two triangles are congruent if two angles and the non-included side of one triangle are equal to the corresponding parts of another triangle.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem used to prove that two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding parts of another triangle.

Front

What is the AAS theorem used for?

Back

The AAS theorem is used to prove that two triangles are congruent based on two angles and a non-included side.

Front

What is the ASA theorem used for?

Back

The ASA theorem is used to prove that two triangles are congruent based on two angles and the included side.

Front

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

Back

No, knowing only one angle and one side is not sufficient to prove triangle congruence; at least two angles or two sides must be known.

Front

What is the difference between AAS and ASA?

Back

AAS involves two angles and a non-included side, while ASA involves two angles and the included side.

Front

What does it mean for triangles to be congruent?

Back

Triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

What theorem can be used if no congruence criteria apply?

Back

If no congruence criteria apply, the triangles may not be congruent, and other methods such as the Law of Sines or the Law of Cosines may be needed.

Front

What is the significance of congruence in geometry?

Back

Congruence is significant in geometry as it allows for the comparison of shapes and sizes, ensuring that two figures can be superimposed on each other.

Front

What is the Side-Angle-Side (SAS) theorem?

Back

The SAS theorem states that if two sides and the included angle of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent.