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 requires the included side between the two angles to be equal, while AAS allows for the side to be non-included.

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 significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal, allowing for various applications in proofs and real-world problems.

Front

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

Back

If two triangles have two pairs of congruent angles, the third pair of angles must also be congruent, making the triangles similar, but not necessarily congruent unless a side is also known.

Front

What theorem can be used to prove triangle congruence if two angles and the included side are known?

Back

The ASA theorem can be used to prove triangle congruence if two angles and the included side are known.

Front

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

Back

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

Front

What is the criteria for triangle congruence using the AAS theorem?

Back

The criteria for triangle congruence using the AAS theorem is that two angles and a corresponding non-included side must be equal to those of another triangle.

Front

What is the criteria for triangle congruence using the ASA theorem?

Back

The criteria for triangle congruence using the ASA theorem is that two angles and the included side must be equal to those of another triangle.