Geometry Formulas Flashcards
center radius form
(x-h)^2 + (y-k)^2 = r^2
standard form
x^2 + y^2 + x term + y term + number term = 0
length of chords
(part1)(part 2) = (part1)(part2)
length of secants and tangent
(outside)(whole) = (outside)(whole)
central angle
central angle = arc
inscribed angle
inscribed angle = 1/2 arc
interior angle
interior angle = (arc+arc) / 2
exterior angle
exterior angle = (arc - arc) / 2
converting: degree to radian
deg/180 = radian / pi
arc length
arc length = (degrees/360) (pi x d)
area of a sector
area of sector = (deg/360) (pi r^2)
slope formula
slope = y2-y1 / x2 -x1 = rise/run
midpoint formula
(x1+x2 / 2, y1+y2 / 2)
distance formula
d = square root of (x2-x1) ^2 + (y2-y1)^2
equation of a line
y = mx+b m= slope b=y-intercept
directed line segment
x = starting x + (fraction) (change in x)
y = starting y + (fraction) (change in y)
area of a trapezoid
a = 1/2h(b1 + b2)
population density
population density = population/area
density
degree of compactness of a substance Mass divided by volume
volume of a rectangular prism
v = l x w x h
volume of a cube
v = e^3
altitude proportion
proj/alt = alt/proj
leg proportion
proj/leg = leg/whole hyp.
sin angle
opposite/hypotenuse
cos angle
adjacent/hypotenuse
tan angle
opposite/adjacent
law of sines
a/sin a = b/sin b = c/sin c
sine and cosine are _____ for complementary angles
equal
scale factor
scale factor = image/preimage or new/old
scale factor
scale factor = image/preimage or new/old
median of a trapezoid
1/2 (base1 + base2)
rotational symmetry
360/#of ways it can sit there and look the same
horizontal and vertical lines
Horizontal line
O slope (zero slope)
Y = # is the equation of every horizontal line
Vertical lines
Undefined slope (no slope)
X = # is the equation of every vertical line
rules of the lengths of the sides of any triangle
given 3 sides:
small side + small side > largest side
given 2 sides:
difference < 3rd side < sum
sum of interior angles of a polygon
sum = 180 (n -2)
sum of exterior angles of a polygon
sum = 360
one interior of a regular polygon
180 (n-2) / n
one exterior angle of a regular polygon
1 exterior angle = 360/n
adjacent interior and exterior angles of a polygon
interior angle + exterior angle = 180
