unit 7.4 geo

Ratio

A comparison of two quantities using division

Proportion

An equation that states two ratios are equal

Means Extremes Property or Cross Multiplying

If A over B equals C over D then A times D equals B times C

Property of Proportions

Manipulating any of the ratios

Similar Polygons

Two figures that have the same shape but not necessarily the same size

Corresponding Angles of Similar Polygons are Congruent

CASPC

Corresponding Sides of Similar Polygons are Proportional

CSSPP

AA ~ Postulate

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

SAS Similarity Theorem

If one angle of a triangle is congruent to one angle of another triangle and the sides including those angles are proportional then the triangles are similar

SSS ~ Th

If the sides of two triangles are proportional then the triangles are simila

CSSPP has to be corresponding (diff triangles)

TPT (Triangle Proportional Th.)

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

TPT Corollary

If 3 parallel lines intersect two transversals, then they divide the transversals proportionally.

Triangle < Bisector Th.

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