Triangle Proportionality, and Similarity: Side-Side-Side, Side-Angle-Side, Angle-Angle, Triangle Midpoint Segment Theorem, and Proportionality in Parallel Lines Cut by Transversal.

Have you experience to be trying to solve a problem that has several triangles embedded in the figure, and you are required to find why some of them are similar, and in this way find the side lengths of those triangles in the figure? Sounds complicated?

This lesson takes the complexity out of it. You will learn the triangle similarity theorems with a lot of visual help to follow all the show. You will view in detail how the proportions are setup and solved. In suggested problems the opportunity of interacting with the lesson is given by solving the companion problems using your stylus on the screen and the marker tools menu. You will like it!

Lesson's Content

Lesson In PDF Format (no animations)


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.

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.

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.


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