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 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 included angle 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 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 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

Can AAA be used to prove triangle congruence?

Back

No, AAA (Angle-Angle-Angle) cannot be used to prove triangle congruence because it only shows that the triangles are similar, not necessarily congruent.

Front

If two triangles have two angles of one triangle equal to two angles of another triangle, what can be concluded?

Back

The triangles are similar by the AA (Angle-Angle) similarity postulate, but not necessarily congruent.

Front

What is the relationship between AAS and ASA?

Back

AAS and ASA are both triangle congruence postulates that can be used interchangeably to prove triangle congruence.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence.

Front

How can you prove triangles are congruent using SSS?

Back

To prove triangles are congruent using SSS, show that all three corresponding sides of the triangles are equal in length.