Triangle Congruence

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 are the criteria for triangle congruence?

Back

The criteria for triangle congruence include: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL) for right triangles.

Front

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

Back

Two triangles are congruent using the SSS criterion if all three sides of one triangle are equal to the three sides of the other triangle.

Front

What does the SAS criterion state for triangle congruence?

Back

The SAS criterion 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

Explain the ASA criterion for triangle congruence.

Back

The ASA criterion 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 AAS criterion for triangle congruence?

Back

The AAS criterion 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 HL criterion for triangle congruence?

Back

The HL criterion 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 triangles are congruent.

Front

How do you identify corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are the angles and sides that match up when the triangles are superimposed on each other.

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, typically written in the form of triangle names, such as ΔABC ≅ ΔDEF.

Front

What is the importance of congruence in geometry?

Back

Congruence is important in geometry because it allows us to determine that two shapes are identical in size and shape, which is essential for solving problems involving geometric figures.