ASA, AAS, and HL postulate

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a postulate that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

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 congruent to two angles and the corresponding 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 postulate that applies to right triangles. It states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right 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 congruent to two sides and the corresponding included angle 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 congruent to all three sides of another triangle, then the triangles are congruent.

Front

If two triangles have two angles congruent, what additional information is needed to prove they are congruent using AAS?

Back

You need to know that one of the non-included sides is congruent.

Front

How can you determine if two triangles are congruent using the ASA postulate?

Back

You need to show that two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle.

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, often written in the form ΔABC ≅ ΔDEF.

Front

What is the significance of the included angle in the ASA postulate?

Back

The included angle is the angle formed between the two sides that are being compared; it is crucial for establishing congruence in the ASA postulate.

Front

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

Back

No, you need at least two angles and one side (AAS) or two sides and the included angle (ASA) to prove congruence.