Triangle Congruence Theorems

Front

What does the HL theorem stand for in triangle congruence?

Back

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

Front

What does the SSS theorem state in triangle congruence?

Back

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

Front

What does the ASA theorem stand for in triangle congruence?

Back

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

Front

What is the definition of triangle congruence?

Back

Triangle congruence means that two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What is the importance of triangle congruence theorems in geometry?

Back

Triangle congruence theorems are important because they provide criteria to determine whether two triangles are congruent, which is fundamental in solving various geometric problems.

Front

Can two triangles be congruent if only one side is equal?

Back

No, two triangles cannot be congruent if only one side is equal; at least two sides and the included angle or three sides must be equal.

Front

What is the difference between ASA and AAS in triangle congruence?

Back

ASA (Angle-Side-Angle) requires two angles and the included side to be equal, while AAS (Angle-Angle-Side) requires two angles and a non-included side to be equal.

Front

What is the criteria for using the SAA theorem in triangle congruence?

Back

SAA (Side-Angle-Angle) states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

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

Back

The included angle in the ASA theorem is significant because it is the angle formed between the two sides being considered, which is crucial for establishing congruence.

Front

How can you determine if two triangles are congruent using the SSS theorem?

Back

To determine if two triangles are congruent using the SSS theorem, measure all three sides of both triangles and check if they are equal.