Postulate 1: Ruler Postulate
The points on a line can be matched one to one with real numbers. The real number that
corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB
is the absolute value of the difference between the coordinates of A and B.
Postulate 2: Segment Addition Postulate
If B is between A and C, then AB + BC = AC. If AB + BC = AC, B is between A and C.
Distance Formula: If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the distance between
A and B is AB =
(𝑥
2
2
− 𝑥 1)
2
2
+ (𝑦
2
2
− 𝑦 1)
2
Pythagorean Theorem: 𝑎 + 𝑏 = 𝑐
Postulate 3: Protractor Postulate
The measure of ⦣AOB is equal to the absolute value of the difference between the real numbers
for line OA and line OB.
Postulate 4: Angle Addition Postulate
If P is in the interior of ⦣RST, then m⦣RSP + m⦣PST = m⦣RST
Midpoint formula: if A (𝑥 1, 𝑦 1) and B(𝑥 2, 𝑦 2)are points in a coordinate plane, then the midpoint of
AB has coordinates
(𝑥 2− 𝑥 1)
2
,
(𝑦 2− 𝑦 1)
2
SQUARE
Sidelength s
P = 4s
2
A= 𝑠
RECTANGLE
Length l land with w
P = 2l +2w
A = lw
TRIANGLE
Side lengths a, b, and c, base b, height h
P = a+b+c
A=
1
2
bh
CIRCLE
Radius r
C = 2πr
2
A = π𝑟