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17 Cards in this Set

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ratio
the ratio of x to y (y can't=0)is x/y and is sometimes written x:y. It is expressed in simplest form.
proportion
an equation stating that two ratios are =.
term of a proportion
a proportion in the form a/b=c/d; a is the first term, b is the second and so on.
extended proportion
an equation showing that three or more ratios are =
extremes of a proportion
the first and last terms
means of a proportion
the middle terms
means-extremes property of proportions
the product of the means = the product of the extremes
Properties of Proportions
1. a/b=c/d is equivalent to
a) ad=bc b) a/c=b/d c) b/a= d/c
d)(a+b)/b= (c+d)/d
2. if a/b=c/d=e/f=..., then a+c+e+.../b+d+f+...=a/b=...
two polygons are similar if...
their vertices can be paired so that:
1) <-. angles are congruent
2)<-> sides are in proportion
scale factor
if two polygons are similar, then the ratio of the lengths of two <->sides
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 trianle 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
divided proportionally
If points L and M lie on line AB and line CD, respectively, and AL/LB=CM/MD, then line AB and line CD are divided proportionally
Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides those side proportionally
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