Triangle Congruence

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the acronym AAS stand for in triangle congruence?

Back

Angle-Angle-Side; a postulate that states if two angles and the non-included side of one triangle are equal to two angles and the non-included side of another triangle, then the triangles are congruent.

Front

What is the SAS postulate?

Back

Side-Angle-Side; a postulate that states 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

What is the SSS postulate?

Back

Side-Side-Side; a postulate that states if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What does the HL theorem stand for?

Back

Hypotenuse-Leg; a theorem that states 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

What is the AAA criterion?

Back

Angle-Angle-Angle; a criterion that states if all three angles of one triangle are equal to all three angles of another triangle, the triangles are similar but not necessarily congruent.

Front

How do you write a congruence statement for triangles?

Back

Front

What is the relationship between congruence and similarity in triangles?

Back

Congruent triangles are similar, but similar triangles are not necessarily congruent; similarity only requires equal angles and proportional sides.

Front

What is the significance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which is essential for proving triangle congruence.

Front

How can you prove that two triangles are congruent using the AAS postulate?

Back

By showing that two angles and the non-included side of one triangle are equal to two angles and the non-included side of another triangle.