# Triangle Congruence Proofs In Two Columns Using SSS, SAS, ASA, AAS, and HL.

### This lesson has a promise: You won't get lost in the middle of the proof. The proofs are solved with a great detailed in explaining each one of the steps, by highlighting them with animations and colors. It is like having somebody to walk you over the solution! Don't miss to take advantage of interacting inside the lesson trying the assigned problems after each example writing them (stylus) on the screen and using the marker tools menu!

Lesson's Content

Lesson In PDF Format (no animations)

Lesson's Glossary

Angle-angle-side (AAS) congruence states that if any two consecutive angles of a triangle are equal in measure to two consecutive angles of another triangle and a pair of corresponding not included sides to these angles is congruent; then the two triangles are congruent; that is, they have exactly the same shape and size.

Angle-side-angle (ASA) congruence states that if any two angles of a triangle are equal in measure to two angles of another triangle and the side in between each pair of angles have the same length, then the two triangles are congruent; that is, they have exactly the same shape and size.

Included angle
The angle made by two consecutive sides of a polygon.

Included side
The side between two consecutive angles in a polygon.

Postulate
A statement assumed to be true without proof.

Proof
A sequence of justified conclusions used to prove the validity of an if-then statement.

Side-angle-side (SAS) congruence states that if any two sides of a triangle are equal in length to two sides of another triangle and the angles between each pair of sides have the same measure, then the two triangles are congruent; that is, they have exactly the same shape and size.

The side-side-side (SSS) congruence states that if the three sides of one triangle have the same lengths as the three sides of another triangle, then the two triangles are congruent.

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