Congruence

Front

What is congruence in geometry?

Back

Congruence in geometry refers to the idea that two figures have the same shape and size. This means that one can be transformed into the other through rotations, translations, or reflections.

Front

What are the criteria for triangle congruence?

Back

The criteria for triangle congruence include: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA), 4) Angle-Angle-Side (AAS), and 5) 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 in length to the three sides of the other triangle.

Front

What does the SAS criterion for triangle congruence state?

Back

The SAS criterion states that if two sides of one triangle are equal to two sides of another triangle, and the included angle between those sides is also equal, 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

Define the HL criterion for triangle congruence.

Back

The HL criterion applies to right triangles and states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two figures are congruent. It typically lists the corresponding parts of the figures in order, such as triangle ABC is congruent to triangle DEF, written as ΔABC ≅ ΔDEF.

Front

How do you identify corresponding angles in congruent triangles?

Back

Corresponding angles in congruent triangles are the angles that occupy the same relative position at each intersection where the sides of the triangles meet.

Front

What is the significance of congruence in real-world applications?

Back

Congruence is significant in real-world applications such as architecture, engineering, and design, where precise measurements and shapes are crucial for functionality and aesthetics.