GEOMETRY Formulas

Area of a triangle

A=1/2bh

Area of a circle formula

A=πr²

Circumference Formula

C = 2πr

Distance Formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Pythagorean Theorem Formula

a² + b² = c²

Equation of a circle in standard form

(x-h)² + (y-k)²= r²

Arc Length Formula

L = 2πr (m⁰/360⁰)

Sector Area Formula

A = (m° / 360) ( πr^2 )

m = central angle

Area of a rectangle formula

A= length x width

Polygon Interior Angles Theorem

(n-2)180

Polygon Exterior Angle Sum Theorem

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

triangle midsegment

A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side

Trapezoid Midsegment

1/2 (base 1 + base 2)

Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of its intercepted arc

central angle of a circle

an angle whose vertex is the center of the circle

Volume of a rectangular prism

V = lwh

Volume of a triangular prism

V=(1/2bh)h

Volume of a cylinder

V=πr²h

Volume of a cone

1/3πr²h

Volume of a rectangular pyramid

V=1/3lwh

Volume of a triangular pyramid

V=1/3(1/2bh)h

Volume of a sphere

V=4/3πr³

Volume of a hemisphere

V=2/3πr³

trigonometry functions

SOH CAH TOA

sine ratio

opposite/hypotenuse

cosine ratio

adjacent/hypotenuse

tangent ratio

opposite/adjacent

Law of Sines

sinA/a = sinB/b = sinC/c

Law of Cosines

a²=b²+c²-2bcCosA

angles formed by transversals

- corresponding angles

- alternate interior angles

- alternate exterior angles

- consecutive interior angles

Angles formed by intersecting chords (inside circle)

(Big Arc + Small Arc) / 2

Angles formed by secant lines (outside circle)

(Big Arc - Small Arc) / 2

slope formula

(y₂- y₁) / (x₂- x₁)

Equation of a line

y=mx+b

point slope form

y - y1 = m(x - x1)

remote interior angles

the sum of the angles of a triangle that are not adjacent to a given exterior angle are equal to the exterior angle.

Chord Segments Theorem

If two chords intersect in a circle, then the products of the lengths of the chord segments are equal. ex) a(b)=c(d)

secant segment

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

surface area of a rectangular prism

1. The sum of all the areas of all the faces or surfaces that enclose a solid. 2. The sum of all the areas of all surfaces of a solid.

corresponding angles

lie on the same side of the transversal and in corresponding positions

alternate interior angles

angles between 2 lines and on opposite sides of a transversal

Alternate Exterior Angles Converse Theorem

If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

same side interior angles

two interior angles on the same side of the transversal

Same Side Exterior Angles

two Exterior angles on the same side of the transversal

Surface area of a cylinder formula

2πr² + 2πrh

Surface Area of a Cone

SA=πrl+πr²

Surface Area of a Pyramid

1/2Pl + B

Surface area of a sphere

4πr²