Congruent Triangle Proofs

Front

What are congruent triangles?

Back

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

Front

What does ASA stand for in triangle congruence?

Back

Angle-Side-Angle; a method to prove triangles congruent by two angles and the included side.

Front

What does AAS stand for in triangle congruence?

Back

Angle-Angle-Side; a method to prove triangles congruent by two angles and a non-included side.

Front

What does SAS stand for in triangle congruence?

Back

Side-Angle-Side; a method to prove triangles congruent by two sides and the included angle.

Front

What are alternate interior angles?

Back

Angles that are on opposite sides of a transversal and inside the two lines it intersects; they are equal when the lines are parallel.

Front

What are vertical angles?

Back

Angles that are opposite each other when two lines intersect; they are always equal.

Front

What is the Angle Bisector Theorem?

Back

A theorem stating that the angle bisector of an angle in a triangle divides the opposite side into segments that are proportional to the other two sides.

Front

What is the significance of corresponding parts of congruent triangles?

Back

If two triangles are congruent, then all their corresponding sides and angles are equal.

Front

What is the definition of triangle congruence?

Back

Two triangles are congruent if their corresponding sides and angles are equal.

Front

What is the criteria for proving triangles are not congruent?

Back

If none of the congruence criteria (ASA, AAS, SAS, SSS, or HL) can be applied, the triangles cannot be proven congruent.