Triangle Congruence

Front

What is the Reflexive Property in triangle congruence?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For triangles, this means that triangle ABC is congruent to triangle ABC.

Front

Define SAS (Side-Angle-Side) congruence criterion.

Back

SAS states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

Explain the AAS (Angle-Angle-Side) congruence criterion.

Back

AAS 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 triangles are congruent.

Front

What is the SSS (Side-Side-Side) congruence criterion?

Back

SSS states that if all three sides of one triangle are congruent to all three sides of another triangle, then the two triangles are congruent.

Front

What is the Vertical Angles Theorem?

Back

The Vertical Angles Theorem states that when two lines intersect, the opposite (vertical) angles are congruent.

Front

How can you determine if two triangles are congruent using the Transitive Property?

Back

If triangle A is congruent to triangle B, and triangle B is congruent to triangle C, then triangle A is congruent to triangle C.

Front

What additional information is needed to prove triangles congruent using HL (Hypotenuse-Leg)?

Back

To use the HL criterion, you need to know that the triangles are right triangles and that the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle.

Front

What does SSA stand for, and why is it not a congruence criterion?

Back

SSA stands for Side-Side-Angle. It is not a congruence criterion because it can lead to ambiguous cases where two different triangles can be formed.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles are significant because they have the same size and shape, allowing for the transfer of properties and measurements between them.