Triangle Congruence Theorems

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the SAS (Side-Angle-Side) theorem state?

Back

The SAS theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle is also congruent, then the triangles are congruent.

Front

What does the ASA (Angle-Side-Angle) theorem state?

Back

The ASA theorem states that if two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent.

Front

What does the AAS (Angle-Angle-Side) theorem state?

Back

The AAS theorem states that 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 the SSS (Side-Side-Side) theorem state?

Back

The SSS theorem states that if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What does the HL (Hypotenuse-Leg) theorem apply to?

Back

The HL theorem applies specifically 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

How do you denote congruent angles?

Back

Front

How do you denote congruent segments?

Back

Front

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

Back

The included angle in the SAS theorem is crucial because it is the angle formed between the two sides being compared. It ensures that the triangles are not only the same size but also oriented in the same way.

Front

What is the difference between SSA and the other congruence theorems?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence because the angle can be opposite a different side, leading to ambiguous cases.