Formulas Involving Polygons

Triangle

4

Quadrilateral

5

Pentagon

6

Hexagon

7

Heptagon

8

Octagon

9

Nonagon

10

Decagon

12

Dodecagon

15

Pentadecagon

n

n-gon (number of sides - gon)

Midline Theorem

A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side

No Choice Theorem

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent

AAS

If there exists a correspondence between the vertices of two triangles such that two angles and a nonincluded side of one are congruent to the corresponding parts of the other, then the triangles are congruent

The sum Si of the measures of the angles of a polygon with n sides is given by the formula:

si=(n-2)180

If one exterior angle is taken at each vertex the sum Se of the measures of the exterior angles of a polygon is given by the formula:

Se=360

The number d of diagonals that can be drawn in a polygon of n sides is given by the formula:

d= n(n-3)/2

The measure of E of each exterior angle of an equiangular polygon of n sides is given by the formula

E= 360/n

regular

both equilateral and equiangular

regular quadrilateral

square

regular triangle

equilateral triangle

1 interior angle equation

I=180(n-2)/n

What is the sum of exterior angles?

360 (Se=360)

Ace