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The sum of angles in a polygon = 180 (n - 2), where n = number of sides. This can also be written as: 180 + 180 (n-3). (Basically you add in another triangle when adding a side to polygon)
Definitions:
Centroid of a triangle - center (where the lines bisecting each angle will meet)
Area of a triangle = base*height/2
Heron's formula - area of any triangle, with sides of length a,b,c, don't know height
semiperimeter (sp) = perimeter/2 = (a+b+c)/2 area = √(sp(sp-a)(sp-b)(sp-c))
Theorems to prove triangles are congruent:
if two chords AB, CD intersect at P, then AP * PB = CP * PD
Interior angle = 1/2 of intercepted arc
all inscribed angles going to the two same points on the circle have the same angle angle of intersecting secants theorem: angle formed by the secant intersection = (opposite arc - adjacent arc)/2
An angle outside the circle with two secants (or tangents) will have an angle
that is 1/2 * (difference of the intercepted arcs)
coterminal angle - the rest of the circle outside the angle.
eg. angle of 30', the coterminal is 330' in radians, use the absolute value. 2pi - |angle|, or |angle| - 2pi for the negative angle
area of an arc:
a = rad*r²/2 .... comes from a = πr² for full circle, and the proportion of a circle in the arc is rad/2π so a = (rad/2π)*(πr²)
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