Triangle Congruence Theorems

Front

What does ASA stand for in triangle congruence theorems?

Back

ASA stands for Angle-Side-Angle, a theorem 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 SAS stand for in triangle congruence theorems?

Back

SAS stands for Side-Angle-Side, a theorem 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 AAS stand for in triangle congruence theorems?

Back

AAS stands for Angle-Angle-Side, a theorem 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 HL stand for in triangle congruence theorems?

Back

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

Front

Which triangle congruence theorem is not valid?

Back

AAA (Angle-Angle-Angle) is not a valid triangle congruence theorem because it does not guarantee that the triangles are congruent; it only shows that they are similar.

Front

How do you name a triangle congruent to triangle ABC?

Back

You can name it triangle FMN if the corresponding vertices are F, M, and N.

Front

If triangle XYZ is congruent to triangle XWZ, what can you say about their corresponding angles and sides?

Back

The corresponding angles and sides of triangle XYZ and triangle XWZ are congruent.

Front

What additional information is needed to prove two triangles are congruent by ASA?

Back

You need to show that the two angles and the included side are congruent, or provide the measures of the angles and the length of the side.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles are significant because they allow us to establish that two shapes are identical in size and shape, which is essential for solving many geometric problems.

Front

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

Back

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