Triangle Similarity That Involves Special Segments, and Perimeters in Triangles. Angle Bisector Theorem.

We have learnt that similar triangles have corresponding sides that are proportional. This statement may be extended to include medians, altitudes, angle bisectors, and perimeters proportional with these sides.

You will go over a lesson that starts by reviewing similarity highlighting the sides that are corresponding, and setting up extended proportions. Once the review is completed, the lesson shifts to solve problems with special segments. The lesson focuses in the reading process of the text in the examples. Don't miss the opportunity to take advantage of interacting with the lesson solving the suggested problems using your stylus and the marker tools menu. Go and try the lesson!

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary


Altitude of a triangle
The perpendicular segment from a vertex to the line containing the opposite side of a triangle.

Angle bisector
A ray that is in the interior of an angle and forms two equal angles with the sides of that angle.

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.

The segment connecting the vertex of an angle in a triangle to the midpoint of the side opposite it.

Perpendicular bisector
The bisector of a segment perpendicular to it.

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.

A polygon with three sides.






Didn't you find what you were looking for? Do your search here!