Congruent Triangles (AAS, HL, and None)

Front

What is the AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence Theorem states that 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 two triangles are congruent.

Front

What is the HL Congruence Theorem?

Back

The HL (Hypotenuse-Leg) Congruence Theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

When can we use the HL Congruence Theorem?

Back

The HL Congruence Theorem can only be used for right triangles.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which is a method to prove triangle congruence by showing that two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which is a method to prove triangle congruence by showing that two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, which is a method to prove triangle congruence by showing that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which is a method to prove triangle congruence by showing that all three sides of one triangle are congruent to all three sides of another triangle.

Front

Can two triangles be congruent if only two sides are known?

Back

No, knowing only two sides (SSA) does not guarantee triangle congruence; it can lead to ambiguous cases.

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

How do you determine if triangles are congruent using AAS?

Back

To determine if triangles are congruent using AAS, check 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.