Geometry Formula Chart

Distance Formula:

Midpoint Formula:

Slope:

Standard Form of a Linear Equation: Standard Form of a Quadratic Equation:

Ax + By = C ax2 + bx + c = 0

Slope-Intercept Form: Quadratic Formula:

y = mx + b

Point-Slope Form:

y – y1 = m(x – x1)

Triangle Sum Theorem:

Standard Equation of a Circle:

(x – h)2 + (y – k)

2 = r

2

With center at (h, k) and radius r

m∠A + m∠B + m∠C = 180°

Exterior Angle Theorem:

m∠1 = m∠A + m∠B

(x1,y1)

(x2,y2)

(0,b) rise

(y2 – y1)

run

(x2 – x1)

Triangle Midsegment Theorem: Trapezoid Midsegment Theorem:

DE || AC DE = AC MN || AB MN || DC

MN = (AB + CD)

Conversion Between Degrees and Radians: 180° = π radians

Angles of Polygons:

n is the # of sides in the polygon

d is the number of degrees in each angle of

a regular polygon

s is the sum of the measures of the angles

Probability:

Theoretical Probability = Number of Favorable Outcomes

Total Number of Outcomes

Experimental Probability = Number of Successes

Number of Trials

Interior Angles Exterior Angles

Sum

of

Ang

les

s = 180(n – 2) s = 360

Eac

h A

ngle

d = 180(n – 2)

n

d = 360

n

Trigonometry

Pythagorean Theorem:

a

2 + b

2 = c

2

45° – 45° – 90° Triangles: 30° – 60° – 90° Triangles:

Ratios:

sinA = opposite cosA = adjacent tanA = opposite

hypotenuse hypotenuse adjacent

m∠A = sin-1

opposite m∠A = cos-1

adjacent m∠A = tan-1

opposite

hypotenuse hypotenuse adjacent

A

B

C

opposite

adjacent

hypotenuse

Perimeter, Area and Volume Formulas

Square Rectangle Triangle

P = 4s P = 2l + 2w P = a + b + c

A = s2 A = lw A = bh

Circle Parallelogram Trapezoid

C = πd or C = 2πr

A = πr 2

A = bh A = (b1 + b2)h

Rhombus Kite Regular n-gon

A = d1d2 A = d1d2 A = aP

Prism Cylinder Pyramid

LSA = Ph LSA = 2πrh LSA = Pl

SA = 2B + Ph SA = 2πr2 + 2πrh SA = B + Pl

V = Bh V = πr2h V = Bh

where B is the area of the base where B is the area of the base

Cone Sphere

LSA = πrl

SA = πr2 + πrl SA = 4πr

2

V = πr2h V = πr

3

Circles

Angle Measures

Central Angle

Inscribed Angle

Tangent and Intersected Chord

Intersection Inside Circle

Intersection Outside Circle

Intersection Outside Circle

Segment Measures

Intersection Inside Circle

Intersection Outside Circle

Intersection Outside Circle

a° a° a°

2a°

a

b c

d

(a)(c) = (b)(d)

a

b

c

(a)(a) = (b)(b+c)

a° a° b° c°

a = (c - b)

2

a°

a°

b°

c°

a = (c + b)

2

a°

b°

º

c°

a = (c - b)

2

a° 2a°

a b

c

d

(a)(a+b) = (c)(c+d)

Arcs and Chords

Properties of Tangents Inscribed Angle

Using the Diameter Equation of a Circle

(h,k)

(x - h)2 + (y - k)

2 = r

2

r

Transformations

Translation Rules

Coordinate rule:

(x, y) (x + a, y + b)

Vector:

PQ

component form: ⟨a, b⟩

Reflection Rules

If (a, b) is reflected in the x-axis, then its image is the point (a, −b)

If (a, b) is reflected in the y-axis, then its image is the point (−a, b)

If (a, b) is reflected in the line y = x, then its image is the point (b, a)

If (a, b) is reflected in the line y = −x, then its image is the point (−b, −a)

P

Q

‘a’ units right

‘b’ units up

where:

‘a’ is the horizontal move

‘b’ is the vertical move

y = x

y = −x

x

y

Rotation Rules

For rotations around the origin:

When a point (a, b) is rotated counterclockwise

about the origin, the following are true:

For a rotation of 90°, (a, b) (−b, a)

For a rotation of 180°, (a, b) (−a, −b)

For a rotation of 270°, (a, b) (b, −a)

Dilation Rules

Coordinate rule when center of dilation is at the origin:

(x, y) (kx, ky)

Coordinate rule when center of dilation is NOT at the origin:

(x, y) (k(x − a) + a, k(y − b) + b)

where:

Scale factor (k) = new .

original

(x, y) is a point on the figure

(a, b) is the center of dilation

Probability

Theoretical and Experimental Probability:

Theoretical Probability = Number of Favorable Outcomes

Total Number of Outcomes

Experimental Probability = Number of Successes

Number of Trials

Probability of Independent and Dependent Events:

Independent Events: P(A and B) = P(A) ⦁ P(B)

Conditional Probability: P(B|A)

Dependent Events: P(A and B) = P(A) ⦁ P(B|A)

Probability of Compound Events:

Overlapping Events: P(A or B) = P(A) + P(B) − P(A and B)

Disjoint Events: P(A or B) = P(A) + P(B)

Permutations Formula: Combinations Formula:

nPr = n! nCr = n!

(n − r)! (n − r)! r!

n = total number to choose from n = total number to choose from

r = number to choose r = number to choose