ASA, AAS, & HL

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 does HL stand for in triangle congruence?

Back

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

Front

Which triangle congruence theorem is applicable only to right triangles?

Back

HL (Hypotenuse-Leg) is the only theorem that applies specifically to right triangles.

Front

Can AAS be used to prove congruence for right triangles?

Back

Yes, AAS can be used to prove congruence for any triangle, including right triangles.

Front

What is the difference between ASA and AAS?

Back

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

Front

If two triangles have two angles equal and the side opposite one of the angles is equal, what can be concluded?

Back

The triangles are congruent by the AAS theorem.

Front

What is the significance of the SSA condition in triangle congruence?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases.

Front

What is the criteria for using the HL theorem?

Back

The HL theorem can only be used when both triangles are right triangles and the hypotenuse and one leg are known to be equal.

Front

If two triangles have two sides equal and the included angle is not equal, what can be concluded?

Back

The triangles are not necessarily congruent; this is known as the SSA condition.