Math by Grades

Math by Topics

$Math Word Problems$

$Probability$

$Set Theory$

Math Worksheets $Math Worksheets$

Math for Specific Tests $SAT Math$
$ACT Math$
$GMAT Math$
$GRE Math$
$High School, Regents$

Math Fun and Games $Math Trivia$
$Math Games$

Exam Preparation

Math in Video Lessons $Basic Algebra$

$Engineering Math$
$Singapore Math$
Science

Others

$What's New$

Similar Triangles and Polygons

A series of free High School Geometry Video Lessons from Brightstorm.

Proportional Segments Between Parallel Lines
When a line is drawn parallel to one side in a triangle, two similar triangles are formed because corresponding angles yield the AA similarity shortcut. Because the triangles are similar, the segments formed by the parallel line are proportional segments. When finding one of the bases of the triangles, be careful in setting up the proportion since the ratio is equal to the small triangle's side to the large triangle's.

Corresponding Parts of Similar Triangles
If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of the angle bisectors, altitudes, and medians of the two triangles. To find a missing angle bisector, altitude, or median, use the ratio of corresponding sides.

Angle Bisectors and Opposite Side Ratios
When an angle bisector is drawn in a triangle, the ratio of the opposite sides forming the bisected angle is equal to the ratio of the segments formed by bisector intersecting the opposite side. This ratio applies to all types of triangles and for an angle bisector drawn from any angle.

Similarity and Area Ratios
If two triangles are similar, then their corresponding sides are proportional. Since sides are a length and lengths are one dimensional, the side ratio will not predict the ratio of the areas. To find the area ratios, raise the side length ratio to the second power. This applies because area is a square or two-dimensional property.

Similarity and Volume Ratios
If two solids are similar, then their corresponding sides are all proportional. The ratio of their surface areas is the side ratio squared and note that the ratios of the areas does not give the actual surface areas. The volume ratio for the two solids is the side length ratio raised to the third power. Again, this is not the solids' volume, only the ratio of the volumes.

Custom Search

We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page.

Custom Search

Amazon.com Widgets