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 the non-included side of one triangle are congruent to two angles and the 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 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 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 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 difference between AAS and ASA?

Back

AAS involves two angles and a non-included side, while ASA involves two angles and the included side.

Front

Can SSA (Side-Side-Angle) prove triangle congruence?

Back

No, SSA does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which allows for the application of various geometric properties and theorems.

Front

How can you prove triangles are congruent using the SAS postulate?

Back

To prove triangles are congruent using SAS, show that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Front

What is an example of using the AAS postulate?

Back

If triangle ABC has angles A and B congruent to angles D and E in triangle DEF, and side AC is congruent to side DF, then triangles ABC and DEF are congruent by AAS.