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Similar Triangles and Polygons

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

Solving Proportions
Solving proportions is a crucial skill when studying similar polygons. The ratio of corresponding side lengths between similar polygons are equal and two equivalent ratios are a proportion. For solving proportions problems, we set up the proportions and solve for the missing side length - it will be a variable, or a variable expression.

Properties of Similar Polygons
Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio (in other words, if they are proportional). Typically, problems with similar polygons ask for missing sides. To solve for a missing length, find two corresponding sides whose lengths are known. After we do this, we set the ratio equal to the ratio of the missing length and its corresponding side and solve for the variable.

Triangle Similarity
There are four triangle congruence shortcuts: SSS, SAS, ASA, and AAS. We have triangle similarity if (1) two pairs of angles are congruent (AA) (2) two pairs of sides are proportional and the included angles are congruent (SAS), or (3) if three pairs of sides are proportional (SSS). Notice that AAA, AAS, and ASA are not listed -- to include them would be redundant since they all have two congruent angles.

Similar Triangles in Circles and Right Triangles
Two triangles in a circle are similar if two pairs of angles have the same intercepted arc. Sharing an intercepted arc means the inscribed angles are congruent. Since these angles are congruent, the triangles are similar by the AA shortcut. If an altitude is drawn from the right angle in a right triangle, three similar triangles are formed, also because of the AA shortcut.

Indirect Measurement
Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures. Two common ways to achieve indirect measurement involve (1) using a mirror on the ground and (2) using shadow lengths and find an object's height. Method 1 measures the person's height and the distances between the person, mirror, and object. Method 2 measures shadows and the person's height

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