point slope

y-y1=m(x-x1)

perpendicular

lines that intersect at right angles, slope is opposite reciprocal

solving by substitution

-solve one of the equations for one of the variables

-substitute the expression into the other equation

-solve

-find the value of the other variable

-check (this is where the lines cross)

-substitute the expression into the other equation

-solve

-find the value of the other variable

-check (this is where the lines cross)

vertex

-b/2a

zeroes

substitute y as 0

quadratic formula

[-b ± √(b² - 4ac)] / (2a)

factoring

x problem set, top=c, bottom=b

factoring when a=/=1

x problem set + box set, top left=a, top right& bottom left=x set answers, factor

line of symmetry

subtract zeroes, divide by 2

rotation

(mathematics) a transformation in which the coordinate axes are rotated by a fixed angle about the origin

reflection

A transformation that "flips" a figure over a mirror or reflection line.

translation

A transformation that "slides" each point of a figure the same distance in the same direction.

distance formula

d = √[( x₂ - x₁) + (y₂ - y₁)]

properties of kites

1) two disjoint pairs of consecutive sides are congruent by definition 2) the diagonals are perpendicular 3) one diagonal is the perpendicular bisector of the other 4) one of the diagonals bisects bisects a pair of opposite angles 5) one pair of opposite angles are congruent

midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

triangle congruence

SSS, SAS, ASA, AAS, and HL

similar polygons

if corresponding angles are congruent and corresponding side lengths are proportional

SohCahToa

SIN (Opposite/Hypotenuse) COS (Adjacent/Hypotenuse) TAN (Opposite/Adjacent)

Area of a Trapezoid

a=1/2h(b1+b2)

Area of a Kite

A=½d₁d₂

inscribed arc

ins=1/2arc

centrical arc

cent=arc

outside angle

big arc - little arc / 2

sum of interior angles

(n-2)180

inside angle

big arc + little arc / 2

30-60-90

A special right triangle with one leg being x, the leg opposite the 60° angle being x√3, and the length of the hypotenuse 2x.

45-45-90

x, x, x√2

exterior angle

360/n