1. Plane Geometry Properties and Relations of Plane Figures
Angles, Parallel Lines, and Perpendicular Lines

2. Triangles
Equilateral Triangle
Isosceles Triangle
Right Triangle
60˚
60˚
60˚
Sum of interior angles in any triangle is always 180˚
Perimeter (P) of a triangle is the sum of the lengths of the sides
Area (A) of triangle is equivalent to ½(base)(height)

3. Special Right Triangles
45˚
60˚ 2x
x√2 x x
30˚
45˚ x
x√3
30˚-60˚-90˚ triangle
45˚-45˚-90˚ triangle
3:4:5
5:12:13
8:15:17
7:24:25
9:40:41

4. Quadrilaterals Parallelogram Opposite sides are of equal lengthb b
height a
base
Area=(base)(height)
Opposite sides are of equal length
Sum of interior angles is 360˚

5. Quadrilaterals RectangleB C A D
Sum of angles is equal to 360˚ because contains 4 right angles
Perimeter (P) of both a parallelogram and a rectangle is equivalent to 2l+2w
Area=(l)(w)
Lengths of the diagonals of a rectangle are congruent, or equal in length

6. Quadrilaterals SquareB C
x√2 x A D
Special rectangle where all four sides are of equal length. All squares are rectangles.
Length of each diagonal of a square is equivalent to the length of on side times √2.

7. Quadrilaterals Trapezoid
Base 2
Height
Base 1
Bases of the trapezoid are never the same length.
Sides of trapezoid may be same length (isosceles trapezoid) or they may not be.
Area=1/2(base1+base2)(height)
When the diagonals of a trapezoid intersect, the ratio of the top of the diagonals to the bottom of the diagonals is the same as the ratio of the top base to the bottom base.

8. Other Polygons Other commonly tested knowledge
Sum of the interior angles of any polygon can be calculated using the formula (n-2)(180˚), where n is the number of sides.
(Pentagon)
(Hexagon)
(Decagon)
=(5-2)(180˚)
=(6-2)(180˚)
=(10-2)(180˚)

9. Circles Area=πr² Circumference= 2πr
Equation of a circle centered at point (h,k) is (x-h)² +(y-k)² = r²
Complete arc of a circle = 360º
The tangent to a circle is a line that touches the circle at exactly one point

10. Angles, Parallel Lines, and Perpendicular Linesb c a
Two lines are parallel if they lie in the same plane and do not intersect
Two lines are perpendicular if their intersection creates right angles f g h k
Vertical angles: a = d = f = k also b = c = g = h
Supplementary angles (they sum 180 °): a,b; c,d; f,g; h,k;
An angle is:
Acute if is smaller than 90 °
Obtuse if is larger than 90 ° but smaller than 180 °
Right angle if is exactly 90°