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 SSS Congruence Postulate?

Back

The SSS (Side-Side-Side) Congruence Postulate states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, which is a method to prove triangle congruence by showing that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which is a method to prove triangle congruence by showing that two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

What is the AAA criterion?

Back

AAA (Angle-Angle-Angle) states that if two triangles have equal corresponding angles, they are similar, but not necessarily congruent.

Front

If ∆ABC≅∆XYZ, what can we say about their corresponding sides?

Back

If ∆ABC is congruent to ∆XYZ, then AB≅XY, BC≅YZ, and AC≅XZ.

Front

What is the difference between similar and congruent triangles?

Back

Similar triangles have the same shape but not necessarily the same size, while congruent triangles have both the same shape and size.

Front

What is the definition of corresponding angles in congruent triangles?

Back

Corresponding angles in congruent triangles are angles that occupy the same relative position at each intersection where a straight line crosses two others.

Front

What is the definition of corresponding sides in congruent triangles?

Back

Corresponding sides in congruent triangles are sides that are in the same relative position in each triangle.

Front

Can two triangles be congruent if they have different angles?

Back

No, two triangles cannot be congruent if they have different angles; all corresponding angles must be equal.