### 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