opposite sides and opposite angles are equal
all sides are equal, opposite angles are equal
one pair of opposite sides is parallel
sum of interior angels of a polygon
(n-2) * 180
Area of a Triangle
(Base * Height)/2
area of a Trapezoid
((Base 1 + Base 2)* Height ) /2
the height refers to a line perpendicular to the 2 bases, which are parallel.
-can also be cut into 2 right triangles and 1 rectangle
Area of any Parallelogram
Base * Height
the height is the line perpendicular to the base, like the trapezoid, you often have to draw in the height.
Area of a Rhombus
(Diagonal 1 * Diagonal 2) /2
the diagonals of a rhombus are Always perpendicular bisectors.
volume of rectangular solid
length width height
The sum of the 3 angles of a triangle
angles correspond to their opposite sides
-this means that the largest angle is opposite the longest, while the smallest angle is opposite the smallest.
-if two sides are equal, their opposite angles are also equal
The Sum of any two sides of a Triangle
must be GREATER than the third side
sum of two sides of a triangle
the length of the 3rd side must lie between the difference and the sum of the two given sides
Common Right Triangle
Isosceles Triangle and the 45-45-90 Triangle
a triangle where two sides and opposite angles are equal.
x - x - x sqrt2
(this triangle is exactly half of a square)
Equilateral Triangle and the 30-60-90 Triangle
two 30-60-90 triangles form an equilateral triangle.
short leg - long leg - hypotenuse
x - x sqrt3 - 2x
diagonal of a square
d = s(sqrt2), where s is a side of the square
diagonal of a cube
d = s(sqrt3), where s is an edge of the cube
corresponding angles are equal and corresponding sides are in proportion
area of similar triangles
if two similar triangles have corresponding side lengths in ratio a:b, then their areas will be in ratio a^2 : b^2
Circumference of a Circle
C = 2pier
Area of a circle
A = pie * r^2
Inscribed vs. Central Angles
An inscribed angle is equal to half of the arc that it intercepts, in degrees.
if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle must be a right triangle
Cylinder Surface Area
SA = 2 circles + rectangle = 2(pier^2) + 2pie*rh
V = pier^2h
Exterior Angles of a Triangle
An exterior angle of a triangle is equal in measure to the sum of the two non-adjacent (opposite) interior angles of the triangle.
the Distance between 2 Points
d = sqrt( ( x2 - x1)^2 + (y2 - y1)^2)
or alternatively, you can draw a triangle by connecting the two points and solve for the hypotenuse.
the perpendicular bisector has the negative reciprocal slope of the line segment it bisects. That is, the product of the two slopes is -1
parallel lines have equal slopes
have negative reciprocal slopes
the Intersection of Two Lines
two lines that intersect share a point that solves both equations.
If two lines in a plane do not intersect, then the lines are parallel.