Geometry Flashcards
Triangle - area
a x ha/2
b x hb/2
c x hc/2
Sum of interior angles of a triangle
180
Isosceles triangle - area
a x ha/2
c x hc/2
Isosceles triangle - height
hc = mc = lc
Equilateral triangle - area
a x ha/2
a^2√3/4
Equilateral triangle - angles
always 60 degrees each
Equilateral triangle - height
a√3/2
Right triangle - area
axb/2
cxhc/2
Pythagorean Triplets
3 4 5
6 8 10
9 12 15
12 16 20
—————-
5 12 13
Special rights triangle - 30 - 60 - 90
30 - 60 - 90
a - a√3 - 2a
Special rights triangle - 45 - 45 - 90
45 - 45 - 90
a - a - a√2
Circle - circumference
2пr
Circle - area
пr^2
Arc of Circle - length
L/360 x circumference
Arc of Circle - sector area
L/360 x area
Trapezoid - area
(a + b) x h/2
Parallelogram - area
a x ha or b x hb
Parallelogram - diagonals
they separate each other into equal halves, but they are not equal, they are not angle bisectors and are not perpendicular
Parallelogram - angles
adjacent angles are supplementary
opposite angles have the same measure
Rectangle - diagonals
diagonals are equal
four isosceles triangles are formed
Rhombus/Diamond - area
a x ha or d1 x d2/2
Rhombus/Diamond - diagonals
d1 and d2 are not equal, but they are angle bisectors and are perpendicular
Square - area
a^2 or d^2/2
Square - diagonals
d = a√2
a diagonal forms a special rights triangle - 45 45 90
Rectangular solid - Surface Area
2ah + 2ab + 2bh
Rectangular solid - Volume
Bh = abh
B = ab = area of the base
Rectangular solid - Diagonal
Longest distance in the figure
D = √a^2 + b^2 + h^2
Cylinder - Surface Area
2(пr^2) + ((2пr) x h)
Cylinder - Volume
Bh = п x r^2 x h
B = п x r^2
Cube - Surface Area
6 x a^2
because we have 6 squares
Cube - Volume
a^3
Cube - Diagonals
D = a√3
d = a√2
Distance between two points
|AB| = √(x1 - x2)^2 + (y1 - y2)^2
Coordinates of Midpoint Segment
M = (x1 + x2/2; y1 + y2/2)
Slope of Line by Equation
y = kx + b
Slope of Line by Two Points
k = y2 - y1/x2 - x1
Two lines are parallel when
k1 = k2
Two lines are perpendicular when
k1 = - 1/k2
the biggest angle of the triangle
is opposite of the biggest side
The sum of all exterior angles
is always 360, for any figure
The sum of all interior angles for any figure
is always (number of angles - 2) x 180
If a triangle is constructed inside a circle and the sides are the chords and the diameter, the angle across will always be
90
