Warm-up Triangle Congruence

Front

What is the definition of triangle congruence?

Back

Triangle congruence means that two triangles are congruent if they have the same size and shape, which can be proven using various congruence criteria.

Front

List the criteria for triangle congruence.

Back

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

Front

If ∆ABC ≅ ∆LMN, what can be said about the corresponding sides and angles?

Back

If ∆ABC ≅ ∆LMN, then AB ≅ LM, BC ≅ MN, AC ≅ LN, and ∠A ≅ ∠L, ∠B ≅ ∠M, ∠C ≅ ∠N.

Front

What does the notation ∆ABC ≅ ∆LMN indicate?

Back

The notation ∆ABC ≅ ∆LMN indicates that triangle ABC is congruent to triangle LMN.

Front

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

Back

To determine if two triangles are congruent using the SSS criterion, measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.

Front

What is the significance of corresponding angles in triangle congruence?

Back

Corresponding angles in triangle congruence are important because if two triangles are congruent, their corresponding angles are equal.

Front

Explain the SAS criterion for triangle congruence.

Back

The SAS criterion states that if two sides of one triangle and the included angle are congruent to two sides of another triangle and the included angle, then the two 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 congruent 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 congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the relationship between the angles and sides in congruent triangles?

Back

In congruent triangles, corresponding angles are equal, and corresponding sides are equal in length.