5.38: AAS and ASA Proofs BW

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem used to prove that two triangles are congruent if two angles and the non-included side of one triangle are equal to the corresponding parts of another triangle.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem used to prove that two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding parts of another triangle.

Front

What is the AAS postulate?

Back

The AAS postulate states that 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 two triangles are congruent.

Front

What is the ASA postulate?

Back

The ASA postulate states that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, then the two triangles are congruent.

Front

Can AAS and ASA be used interchangeably?

Back

Yes, both AAS and ASA can be used to prove triangle congruence, but they apply to different configurations of angles and sides.

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

If ΔDEC ≅ ΔBEA, what can be inferred about their corresponding parts?

Back

If ΔDEC ≅ ΔBEA, then their corresponding angles and sides are equal.

Front

What is the significance of the included side in ASA?

Back

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

Front

What is the significance of the non-included side in AAS?

Back

In AAS, the non-included side is the side that is not between the two angles being considered, and it is essential for establishing congruence.

Front

What is the HL theorem?

Back

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