Triangle Congruence

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 their corresponding sides and angles are equal.

Front

What is the Angle-Angle-Angle (AAA) criterion for triangle congruence?

Back

The AAA criterion states that if two triangles have equal corresponding angles, they are similar, but not necessarily congruent.

Front

What is the Side-Angle-Side (SAS) theorem for triangle congruence?

Back

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

Front

What is the Side-Side-Side (SSS) theorem for triangle congruence?

Back

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

Front

What is the Angle-Side-Angle (ASA) theorem for triangle congruence?

Back

The ASA theorem 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 Angle-Angle-Side (AAS) theorem for triangle congruence?

Back

The AAS theorem 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 a rigid motion in geometry?

Back

A rigid motion is a transformation that preserves distance and angle measures, meaning the shape and size of the figure remain unchanged.

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 mapped onto the other using a series of rigid motions such as translations, rotations, or reflections.

Front

What is the significance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which allows for the application of congruence theorems.

Front

What is the relationship between triangle congruence and similarity?

Back

Triangle congruence implies similarity, but similarity does not imply congruence. Congruent triangles are similar, but similar triangles may not be congruent.