Triangle Congruence Theorems

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 SSS stand for in triangle congruence?

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

What does SAS stand for in triangle congruence?

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 does HL stand for in triangle congruence?

Back

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

Front

What is the AAA criterion in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which states that if three angles of one triangle are congruent to three angles of another triangle, the triangles are similar but not necessarily congruent.

Front

Can two triangles be congruent if only their angles are known?

Back

No, knowing only the angles (AAA) does not guarantee congruence; it only guarantees similarity.

Front

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

Back

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

Front

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

Back

To determine congruence using AAS, check if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means the triangles are identical in size and shape, while similarity means they have the same shape but may differ in size.