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

Most students express the desire of having the proofs explained to them in a friendly manner, so that they can follow the flow in the proof. Why is that reason given in the third, or forth step? Why not in the second? What other statements are prerequisite for this last statement? Why?

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!

Lesson's Content

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.

Theorem
A theorem in mathematics is a proven fact. A theorem about polygon must be true for every polygon; there can be no exceptions. An idea which works in several different cases is not enough.

Interactive Geometric Applets: Relevant Theorems.

"Interior Angle Sum Theorem In A Triangle"

Drag any of the vertices in the triangle below to verify that

the sum is 180° all the time. Check the sum in the upper right corner.

"Supplementary Angles"

Two positive angles that sum 180° are supplementary.

Drag point "C" and verify that the angles are supplementary.

"Alternate Interior Angles Theorem"

In parallel lines cut by a transversal: Alternate interior angles are congruent.

Drag point "B" and verify that alternate interior angles remain congruent.

Vocabulary Puzzle Interactive

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