Triangle Congruence

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, 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 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

How can you use angle bisectors to determine triangle congruence?

Back

If two triangles have an angle bisector that divides the angles into equal parts, and the sides opposite those angles are proportional, the triangles may be congruent.

Front

What role do corresponding parts play in triangle congruence?

Back

Corresponding parts of congruent triangles are equal, meaning that if triangles are congruent, their corresponding sides and angles are also equal.

Front

How can you prove that two triangles are congruent using transformations?

Back

You can prove that two triangles are congruent by showing that one triangle can be transformed into the other through a series of rigid motions, such as translations, rotations, and reflections.