# Two Column Proofs Involving Triangle Similarity and Proportionality.

### In this lesson, you may very well forget about those headaches. We approach two column proofs involving triangle similarity in an innovative way. The proofs to study are presented showing you every single step, and how this is influenced by previous steps... until of the completion of the proof; after the example is over, you will be given the same proof with different labels in the figure, so that you may check your understanding of the solution process. You should really try it!

Lesson's Content

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Lesson's Glossary

Angle-angle-angle (AAA) similarity
The angle-angle-angle (AAA) similarity test states that given two triangles that have corresponding angles that are congruent, then the triangles are similar. As we know the sum of the interior angles in a triangle is 180°, so if two corresponding are congruent, then the other ones should be as well.

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) similarity
The side-angle-side (SAS) similarity test states that given two triangles that have two pairs of sides that are proportional and the included angles are congruent, then the triangles should be similar.

Side-side-side (SSS) similarity
The side-side-side (SSS) similarity test states that for two triangles to be similar; all corresponding sides should be proportional.

Similar
two polygons are similar polygons if corresponding angles have the same measure and corresponding sides are in proportion.

Similar triangles
Similar triangles are triangles which have the same shape but probably different size. Corresponding angles need to be congruent, and corresponding sides are in proportion.

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.

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