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quotient of two numbers


an equation stating that two or more ratios are equal


first and fourth terms


second and third terms

geometric mean

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

means-extremes products therom

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

arithmetic mean

average between two numbers


same shape, different size


shrink, becoming smaller

proving similar trianges

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

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

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

pythagorean theorem


pythagorean triples

any three whole numbers that satisfy the equation a²+b²=c²
TRIANGLES: (3,4,5) (6,8,10) (9,12,15)...etc.

30-60-90 triangle

opposite of 30 = x
opposite of 60 = x√3
opposite of 90 (hypotenuse) = 2x

45-45-90 triangle

opposite of 45's = x
opposite of 90 = x√2

trigonometric ratios

sin <x = opposite leg/hypotenuse
cos <x = adjacent leg/hypotenuse
tang <x = opposite leg/adjacent leg

angle of elevation

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

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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