Congruent Triangles (SSS, SAS, ASA, AAS, HL)

Front

What are congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does SSS stand for in triangle congruence?

Back

Side-Side-Side: If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

Side-Angle-Side: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

Angle-Side-Angle: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

Angle-Angle-Side: 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, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

Hypotenuse-Leg: In right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, the triangles are congruent.

Front

How can you determine if two triangles are congruent?

Back

By using congruence criteria: SSS, SAS, ASA, AAS, or HL.

Front

If two triangles have two equal angles, what can be said about their sides?

Back

The sides opposite those angles are proportional, but the triangles may not be congruent unless a third side is also equal.

Front

What is the significance of the included angle in SAS?

Back

The included angle is the angle between the two sides being compared; it is crucial for establishing congruence.

Front

Can two triangles be congruent if they have two equal sides and a non-included angle?

Back

No, this is known as SSA (Side-Side-Angle) and does not guarantee congruence.