Triangle Congruency Theorems

Front

What does the HL theorem stand for in triangle congruency?

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 leg of another right triangle, then the triangles are congruent.

Front

What is the AAS theorem in triangle congruency?

Back

AAS stands for Angle-Angle-Side theorem, which 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

Define the SAS theorem in triangle congruency.

Back

SAS stands for Side-Angle-Side theorem, which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does the SSS theorem state?

Back

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

Front

What is the difference between ASA and AAS?

Back

ASA (Angle-Side-Angle) requires the included side between two angles to be known, while AAS (Angle-Angle-Side) does not require the included side to be known.

Front

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

Back

To prove triangles are congruent using the HL theorem, show that both triangles are right triangles and that their hypotenuses and one leg are equal.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal, allowing for various geometric proofs and constructions.

Front

Can SSA be used to prove triangle congruency?

Back

No, SSA (Side-Side-Angle) does not guarantee triangle congruency, as it can lead to ambiguous cases.

Front

What is the Angle-Angle (AA) criterion?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar, but not necessarily congruent.

Front

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

Back

In the SAS theorem, the included angle is the angle formed between the two sides being compared, and it is crucial for establishing congruency.