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ratio

quotient of two numbers

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proportions

an equation stating that two or more ratios are equal

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extremes

first and fourth terms

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means

second and third terms

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geometric mean

a over x = x over b

a x

--- = ---

x b x= g.m. between a & b

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means-extremes products therom

product of the means = product of the extremes (cross multipling)

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arithmetic mean

average between two numbers

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similar

same shape, different size

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reduction

shrink, becoming smaller

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proving similar trianges

AA (angle-angle)

SSS (corresponding sides are proportional)

SAS (two corresponding sides are proportional and included angle is congruent)

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side-splitter therom

if a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally

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angle bisector therom

if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides

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pythagorean theorem

a²+b²=c²

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pythagorean triples

any three whole numbers that satisfy the equation a²+b²=c²

TRIANGLES: (3,4,5) (6,8,10) (9,12,15)...etc.

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30-60-90 triangle

opposite of 30 = x

opposite of 60 = x√3

opposite of 90 (hypotenuse) = 2x

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45-45-90 triangle

opposite of 45's = x

opposite of 90 = x√2

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trigonometric ratios

a.k.a. SOHCAHTOA

sin <x = opposite leg/hypotenuse

cos <x = adjacent leg/hypotenuse

tang <x = opposite leg/adjacent leg

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angle of elevation

the angle formed by a horizontal line and the line of sight to an object above the horizontal line

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angle of depression

the angle formed by a horizontal line and the line of sight to an object below the horizontal line

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