Similarity

Simplify Radicals

1. No perfects square factors under radicals
2. No radicals allowed in the denominator of a fraction- evil
3. No fraction under the radicals- bad

Ratio: A Comparison of 2 Numbers

1. Fraction From
2. Colin Form
3. Word Fro

Simplified form for ratio: reduced

Proportion- 2 equal ratios; a & d- extremes, b & c- means

Extended Proportion- a proportion involving three or more ratios

Geometric mean- to find the geometric mean between a, b; a/x=x/b; x- geometric means, a, b- extreme

Similar Polygons- two polygons are similar if they have the exact same shape and proportional sides.

Same Shape - all the corresponding angles are congruent.

Same Size - all the corresponding sides are congruent.

Two polygons are similar (~) if they have the exact same shape and proportional sizes.
Shape is determined by the angles, so all the corresponding angles are congruent.

Size is determined by the side length, so all the corresponding sides are proportional.

Scale Factor - the reduced ratio of corresponding side lengths of similar polygons.

Perimeters are always the same ratio as the sides.

Methods to Prove Two Triangles Similar:

1. AA (Angle - Angle)- If 2 angles in one triangle are congruent in a second triangle, then the triangle are similar; once you know the two triangles are similar, you can find the scale factor and then use it to find missing side length.
2. SAS (Side - Angle - Side) - Show two sides of one triangle are proportional to the corresponding sides of the other triangle, and the included angles are congruent.
3. SSS (Side - Side - Side) - Show all three sides of one triangle are proportional to the corresponding sides of the other triangle.