ASA, AAS, & HL

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a postulate 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 does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a theorem that applies to right triangles, stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the SSA condition in triangle congruence?

Back

SSA stands for Side-Side-Angle, which is not a valid congruence postulate because it does not guarantee triangle congruence.

Front

When can you use the ASA postulate?

Back

You can use the ASA postulate when you know two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

When can you use the AAS theorem?

Back

You can use the AAS theorem when you know two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

Front

When can you use the HL theorem?

Back

You can use the HL theorem when you are dealing with right triangles and know the lengths of the hypotenuse and one leg of both triangles.

Front

What is the difference between ASA and AAS?

Back

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

Front

Can two triangles be congruent if only SSA is known?

Back

No, SSA does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

What is the significance of congruence in triangles?

Back

Congruence in triangles means that the triangles have the same size and shape, allowing for the conclusion that corresponding sides and angles are equal.