Congruent Triangles

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

What is the SAS (Side-Angle-Side) congruence criterion?

Back

The SAS criterion states that if two sides of one triangle are equal to two sides of another triangle, and the angle between those sides is equal, then the triangles are congruent.

Front

What is the SSS (Side-Side-Side) congruence criterion?

Back

The SSS criterion states that if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What is the ASA (Angle-Side-Angle) congruence criterion?

Back

The ASA criterion states that if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the triangles are congruent.

Front

What is the AAS (Angle-Angle-Side) congruence criterion?

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 (Hypotenuse-Leg) congruence criterion for right triangles?

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 can you determine if two triangles are congruent using transformations?

Back

Two triangles are congruent if one can be transformed into the other using a series of rigid motions: translations, rotations, and reflections.

Front

What is the significance of corresponding angles in congruent triangles?

Back

In congruent triangles, corresponding angles are equal, which helps establish the congruence of the triangles.

Front

What is the significance of corresponding sides in congruent triangles?

Back

In congruent triangles, corresponding sides are equal in length, which is a key factor in determining triangle congruence.

Front

How can you prove that two triangles are congruent using the properties of isosceles triangles?

Back

If two sides of a triangle are equal, the angles opposite those sides are also equal, which can help establish congruence with another triangle.