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ratio

quotient of two numbers

proportions

an equation stating that two or more ratios are equal

extremes

first and fourth terms

means

second and third terms

geometric mean

a over x = x over b

a x

--- = ---

x b x= g.m. between a & 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

similar

same shape, different size

reduction

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)

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

a²+b²=c²

pythagorean triples

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

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

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

opposite of 60 = x√3

opposite of 90 (hypotenuse) = 2x

45-45-90 triangle

opposite of 45's = x

opposite of 90 = x√2

opposite of 90 = x√2

trigonometric ratios

a.k.a. SOHCAHTOA

a.k.a. SOHCAHTOA

sin <x = opposite leg/hypotenuse

cos <x = adjacent leg/hypotenuse

tang <x = opposite leg/adjacent leg

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