Geo Chapter 7: Similar Polygons

ratio

A comparison of two quantities by division.

proportion

An equation stating that two ratios are equal

Means-Extremes Property

if a/b=c/d, then ad=bc

Two polygons are similar if:

1. Corresponding angles are congruent

2. Corresponding sides are proportional

Scale Factor

the ratio of the lengths of two corresponding sides of two similar polygons

AA Similarity Postulate

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.

SSS Similarity Theorem

If the sides of two triangles are in proportion, then the triangles are similar.

Triangle Proportionality Theorem

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

A corollary from Triangle Proportionality Theorem

If three parallel lines intersect two transversals,...

then they divide the transversals proportionally.

Triangle Angle-Bisector Theorem

If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides