ASA and AAS Triangle Congruence

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a postulate used to prove that two triangles are congruent if two angles and the included side are equal.

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 SSS postulate?

Back

SSS stands for Side-Side-Side, a postulate that states if all three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

Front

What is the SAS postulate?

Back

SAS stands for Side-Angle-Side, a postulate that states if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does AAA stand for in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which indicates that if all three angles of one triangle are equal to the three angles of another triangle, the triangles are similar, but not necessarily congruent.

Front

Can two triangles be congruent if only one angle and two non-included sides are known?

Back

No, this is known as the SSA condition, which does not guarantee triangle congruence.

Front

What is the significance of the included side in ASA?

Back

In ASA, the included side is the side between the two angles; it is crucial for establishing congruence.

Front

If two triangles have two angles equal and one side equal, what can be concluded?

Back

The triangles are congruent by the AAS theorem.

Front

What is the difference between ASA and AAS?

Back

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

Front

What is the condition for triangle congruence using SSS?

Back

All three corresponding sides of the triangles must be equal.