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Geometry Ch 7 & 8 vocab

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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
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)
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.
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
a.k.a. SOHCAHTOA
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