Proving Triangles Congruent

Front

What does the HL theorem state?

Back

The HL (Hypotenuse-Leg) theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

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 ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence 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 is the AAS criterion for triangle congruence?

Back

AAS stands for Angle-Angle-Side, which 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 SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence 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 is the AAA criterion for triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which indicates that if all three angles of one triangle are congruent to all three angles of another triangle, the triangles are similar, but not necessarily congruent.

Front

What is the significance of the term 'included side' in triangle congruence?

Back

The 'included side' is the side that is between two angles in a triangle. It is crucial in criteria like ASA and SAS for proving triangle congruence.

Front

Can two triangles be proven congruent with only one side and one angle?

Back

No, you need at least two sides and the included angle (SAS) or two angles and the included side (ASA) to prove congruence.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size.

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.