Triangle Congruence Theorems

Front

What does AAA stand for in triangle congruence theorems?

Back

AAA stands for Angle-Angle-Angle, which is NOT a triangle congruence theorem because it does not guarantee that the triangles are congruent.

Front

What is the ASA triangle congruence theorem?

Back

ASA stands for Angle-Side-Angle, which states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What is the SSS triangle congruence theorem?

Back

SSS stands for Side-Side-Side, which states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What is the HL triangle congruence theorem?

Back

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

Front

What is the significance of triangle congruence theorems in geometry?

Back

Triangle congruence theorems are used to prove that two triangles are congruent, which means they have the same size and shape, allowing for the application of various geometric principles.

Front

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

Back

No, knowing only the angles (AAA) does not guarantee congruence, as it can lead to similar triangles that are not congruent.

Front

What is the difference between congruence and similarity in triangles?

Back

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

Front

What is the importance of the included side in the ASA theorem?

Back

The included side is crucial in the ASA theorem because it connects the two angles, ensuring that the triangles are congruent based on the specific configuration.

Front

What conditions must be met to use the SSS theorem?

Back

To use the SSS theorem, all three sides of one triangle must be equal to all three sides of another triangle.

Front

In what scenario can the HL theorem be applied?

Back

The HL theorem can be applied only in right triangles, where the hypotenuse and one leg are known.