Sum of interior angles The sum of interior angles θ of a polygon of n sides is: Sum, Σθ = (n – 2) × 180° Sum of exterior angles The sum of exterior angles β is equal to 360°. ∑β = 360°

A circle is circumscribed about a triangle if it passes through the vertices of the triangle.

Given four sides a, b, c, d, and two opposite angles B and D: Divide the area into two triangles

Circumcenter of the triangle

a b

r c

r=

A = ½ ab sin B + ½ cd sin D

abc 4A T

AT = area of the triangle
Parallelogram Number of diagonals, D The diagonal of a polygon is the line segment joining two non-adjacent sides. The number of diagonals is given by: n D = (n − 3) 2 Regular polygons Circle inscribed in a triangle (Incircle) A circle is inscribed in a triangle if it is tangent to the three sides of the triangle. B Incenter of the triangle

B d1 A

C

θ

d2

b

PLANE GEOMETRY
PLANE AREAS Triangle

D a Given diagonals d1 and d2 and included angle θ: A = ½ d1 × d2 × sin θ Given two sides a and b and one angle A:

r=

B a h c

A = ab sin A
Rhombus

C d1 d2 a

D

C

θ
b
A = ½ bh

A B

90° a A

Polygons whose sides are equal are called equilateral polygons. Polygons with equal interior...

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