General Formulas
Distance Formula: 
((x2 - x1)2 + (y2 - y1)2) where
(x1, y1) and (x2, y2) are
points.
Distance Formula in Space: ((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2) where
(x1, y1, z1) and (x2, y2, z2) are
points.
Midpoint Formula:((A + C)/2), (B + D)/2)) where
(A, B) and (C, D) are the endpoints of the segment.
Midpoint Formula in Space:(((A + D)/2), ((B + E)/2), ((C +
F)/2)) where (A, B, C) and (D, E, F) are the endpoints of the segment.
Perimeter Formulas
Equilateral Polygon Perimeter Formula: n * s,
where n is the number of sides and s is the length of those sides.
Circle Circumference Formula: 
d
where d is the diameter of the circle.
Area Formulas
Triangle Area Formulas: 1/2 * ab * sin(c) where a and b
are sides and c is the enclosed angle; 1/2 * hb where h is the height and b is
the length of the base.
Equilateral Triangle Area Formulas: (s2 * 3)
/ 4 where s is the length of one side.
Right Triangle Area Formula: Half of the product of
the length of the legs.
SSS Triangle Area Formula: the square root of (S(S - a)(S
- b)(S - c)) where a, b, and c are sides and S is (a + b + c)/2
Trapezoid Area Formula: 1/2 * h(l1 + l2) where
h is the altitude and l1 + l2 are the bases.
Parallelogram Area Formula: lh where l is the l is the
length of one of the bases and h is the length of the altitude.
Circle Area Formula: 
r2 where r
is the radius
Pick's Formula: 1/2 * P + I - 1 where P is the
number of points on the polygon and I is the number of points in the polygon if
the polygon is in a coordinate plane.
Right Prism - Cylinder Lateral Area Formula: ph
where the p is the perimeter (circumference) and h is the height
Prism - Cylinder Surface Area Formula: L.A. +
2B where L.A. is the lateral area and B is the area of the base.
Regular Pyramid - Right Cone Lateral Area Formula: 1/2 *
lp where l is the length of the slant height and p is the perimeter of the
base.
Pyramid - Cone Surface Area Formula: the
lateral area plus the area of the base.
Sphere Surface Area Formula: 4
r2 where r
is the radius.
Volume Formulas
Cube Volume Formula: s3 where s
is the length of an edge.
Prism - Cylinder Volume Formula: Bh where B is the area
of the base and h is the height.
Pyramid - Cone Volume Formula: 1/3 * Bh where B is the
area of the base and h is the height.
Sphere Volume Formula: 4/3 * 
r3 where r
is the radius.
Postulates
Postulates are statements that are assumed to be true
without proof. Postulates serve two purposes - to explain undefined terms, and
to serve as a starting point for proving other statements.
Point-Line-Plane
Postulate
A) Unique Line Assumption: Through
any two points, there is exactly one line.
B) Dimension Assumption: Given a
line in a plane, there exists a point in the plane not on that line. Given a
plane in space, there exists a line or a point in space not on that plane.
C) Number Line Assumption: Every line is a set of points that can be put
into a one-to-one correspondence with real numbers, with any point on it
corresponding to zero and any other point corresponding to one.
D) Distance Assumption: On a
number line, there is a unique distance between two points.
E) If two points lie on a plane, the line containing them also lies on
the plane.
F) Through three noncolinear points, there is exactly one plane.
G) If two different planes have a point in common, then their
intersection is a line.
Euclid's Postulates
A) Two points determine a line
segment.
B) A line segment can be extended indefinitely along a line.
C) A circle can be drawn with a center and any radius.
D) All right angles are congruent.
Note: This part has been proven as a theorem.
E) If two lines are cut by a transversal, and the interior angles on the
same side of the transversal have a total measure of less than 180 degrees,
then the lines will intersect on that side of the transversal.
Polygon Inequality Postulates
Triangle Inequality Postulate: The sum
of the lengths of two sides of any triangle is greater than the length of the
third side.
Quadrilateral Inequality Postulate: The sum of the lengths of 3 sides of
any quadrilateral is greater than the length of the fourth side.
Theorems
Theorums are statements that can be deduced and proved
from definitions, postulates, and previously proved theorums.
Line Intersection Theorem: Two
different lines intersect in at most one point.
Betweenness Theorem: If C is between A and B and on 
, then AC + CB = AB.
Related Theorems:
Theorem: If A, B, and C
are distinct points and AC + CB = AB, then C lies on .
Theorem: For any points
A, B, and C, AC + CB 
.
Pythagorean Theorem: a2 + b2 = c2, if c is the hypotenuse.
Right Angle Congruence Theorem: All right angles are congruent.