Math Formulas/Concepts/Principles/Rules

A=s²

Formula for finding the AREA of a SQUARE

P = 4s

Formula for finding the PERIMETER of a SQUARE

A = bh/2

Formula for finding the AREA of a TRIANGLE

P = a + b + c

Formula for finding the PERIMETER of a TRIANGLE

A + lw

Formula for finding the AREA of a RECTANGLE

P = 2l + 2w

Formula for finding the PERIMETER of a RECTANGLE

A = h

Formula for finding the AREA of a PARALLELOGRAM

P = 2a + 2b

Formula for finding the PERIMETER of a PARALLELOGRAM

A = (𝑎+𝑏)/2 × h

Formula for finding the AREA of a TRAPEZOID

P = a + b + c + d

Formula for finding the PERIMETER of a TRAPEZOID

V = s³

Formula for finding the VOLUME of a CUBE

SA = 6s²

Formula for finding the SURFACE AREA of a CUBE

V = 𝜋r²h

Formula for finding the VOLUME of a RIGHT CIRCULAR CYLINDER

SA = 2𝜋rh

Formula for finding the SURFACE AREA of a RIGHT CIRCULAR CYLINDER

V = (1/3)𝜋r²h

Formula for finding the VOLUME of a RIGHT CIRCULAR CONE

SA = 𝜋r √r² + h²

Formula for finding the SURFACE AREA of a RIGHT CIRCULAR CONE

V = bh

Formula for finding the VOLUME of an IRREGULAR PRISM

C= 2πr

Formula for finding the CIRCUMFERENCE of a CIRCULAR REGION

A = πr²

Formula for finding the AREA of a CIRCULAR REGION

V = (4/3)πr³

Formula for finding the VOLUME of a SPHERE

SA = 4πr²

Formula for finding the SURFACE AREA of a SPHERE

acute angle

angle that measures below 90 degrees

right angle

angle that measures 90 degrees

obtuse

angle that measures larger than 90 degrees but less than 180 degrees

straight angle

angle that measures 180 degrees

complementary angles

angles that add up to 90 degrees

supplementary angles

angles that add up to 180 degrees

equal

vertical/opposite angles are ____

common side, vertex

adjacent angles have a __________ and ______

line

a straight path of points that has no beginning or end

ray

contains one endpoint and extends forever in one direction

segment

a portion of a line that has two endpoints

intersecting lines

lines that come together at a point

perpendicular lines

lines that intersect at right angles

parallel lines

lines that are the same distance apart and never meet

transversal lines

lines that crosses two or more lines

180 degrees

the sum of all angles of any triangle is ___

equilateral - three equal angles (all angles are 60 degrees) and three sides of the same length

isosceles - two equal sides and two equal angles

scalene - no equal sides and angles

types of triangles

acute triangles

triangle with angles that measure never more than 90

obtuse triangle

a triangle that contains one angle that measures more than 90 degrees

right trianglea

a triangle that contains a 90 degree angle

two remote interior angles

an exterior angle is equal to the sum of the _______________________

proportional

corresponding sides of similar triangles are ____________

radius

a line that lies from the center to the circle itself

diameter

a line that contains the center and has its endpoints on the circle

secant

a line passing through 3 exact points on a curve

bisect

to divide into two equal sections

congruent

identical in size and shape

pi

a constant equal to 3.14

arc

set of pints that lie on a circle

chord

a line that connects two points on a circle

vertex

the point of intersection between two or more rays, often called a corner

central angle

has its vertex at the center of a circle and its endpoints on the circumference. its degree is equal to that of its intercepted arc

inscribed angle

has its vertex and endpoints on the circumference. its degree is equal to half of its intercepted arc

s= θr

arc length formula if central angle is given in radian

s = (θ/360) x 2πr

arc length formula if central angle is given in degrees

sector = (1/2)rθ

formula for finding sector of circle

sinθ= opp/hyp, cosθ = adj/hyp, tanθ = opp/adj

define SOH CAH TOA

a/sinA=b/sinB=c/sinC

law of sines

a² = b² + c² - bc cos A

b² = a² + c² - ac cos A

c² = a² + a² - ab cos A

law of cosines

cosecant is the reciprocal of sine.

secant is the reciprocal of cosine.

cotangent is the reciprocal of tangent.

reciprocal identities

sin(- θ) = - sine(θ)

cos(- θ) = cos (θ)

tan (- θ) = - tan(θ)

negative angles in trig

sin²θ + cos²θ = 1

1 + tan²θ = sec²θ

1 + cot²θ = csc²θ

pythagorean identities

x(degrees) x π/180

degree to radians

x times 180/π

radians to degrees

a sub 1 can be replaced by any other known position

formula for the nth term of an arithmetic sequence

formula for finding the sum of an arithmetic sequence

a sub 1 can be replaced by any other known position

formula for finding the nth term of a geometric sequence

formula for finding the sum of a finite geometric sequence

formula for finding the sum of an infinite geometric sequence