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polygon interior angles theorem
the sum of the measures of the interior angles of a convex n-gon is (n-2)180°
corollary to polygon interior angles theorem
the measure of each interior angle of a regular n-gon is 1/2(n-2)180°
polygon exterior angles theorem
the sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°
corollary to polygon exterior angles theorem
the measure of each exterior angle of each of the exterior angle of a regular n-gon is 1/n(360°)
area of an equilateral triangle theorem
the area of an equilateral triangle is one fourth the squaere of the length of the side times √3
area of a regular polygon theorem
the area of a regular n-gon with side length s is half the producr of the apothem and the perimeter, so A=1/2a(p)
area of similar polygons theorem
if 2 polygons are similar with the lengths of corresponding sides in the ratio a:b, then the ratio of the area is a²:b²
arc length corollary
in a circle, the ratio of the length of a given arc to the circumference is = the ratio of the measure of the arc to 360°
area of a sector
the ratio of the area of a sector of a circle to the area of the circle is = to the ratio of the measures of the intercepted arc 360°
probability and length
let segment AB be a segment that contains the segment CD. if a point K on segment AB is chosen at random, then the probability that it is on segemtn CD is as follows P(point K is on segment CD)= Legment of segement CD/ length of AB
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