Geometry Cheat Sheet

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the equation for a line is
"y" equals "m" times "x" plus "b"
where "m" is the slope and "b" is the "y" intercept
the slope is the change in "y" over the change in "x"

if "m" equals "m", two lines are parallel
if "m" equals negative one divided by "m", two lines are perpendicular

congruent means to have the same size or shape
pi is approximately three point one four
the diameter of a circle is the radius times two
the circumference of a circle is pi times the diameter

a parallelogram has 4 sides (Quadrilateral)
opposite sides are parallel
pairs of opposite sides and angles are congruent
The rhombus, rectangle, and square are all parallelograms

the perimeter of a rectangle is 2 times length plus 2 times width
the perimeter of a square is 4 times side length

the area of a square is side length squared
the area of a rectangle is length times width
the area of a parallelogram is length times height
the area of a triangle is base times height divided by two
the area of a circle is pi times radius squared

the volume of a sphere is four-thirds times pi times radius to the third
the volume of a cylinder is height times pi times radius squared
the volume of a cone is one-third times pi times radius to the third
the volume of a pyramid is base area times height divided by three
the volume of a cube is side length to the third
the volume of a prism is base area times height

sine is opposite over hypotenuse
cosine is adjacent over hypotenuse
tangent is opposite over adjacent

secant is 1 over the cosine
cosecant is 1 over the sine
cotangent is 1 over the tangent

The Law of Sines is
sine of Alpha over "A" equals sine of Beta over "b" equals sine of Gamma over "c"
where Alpha, Beta, and Gamma are the angles of the triangle
and "A", "b", and "c" are the sides opposite those angles

The Law of Cosines is
"c" squared equals "A" squared plus "b" squared
minus two times "A" times "b" times cosine of Gamma
where "c" is the length of the side opposite Gamma,
"A" and "b" are the lengths of the other two sides,
and Gamma is the angle between sides "A" and "b".

Pythagorean Theorem is "A" squared plus "b" squared equals "c" squared
To get distance,
take the change in "x" squared and add it to the change in "y" squared
then take the square root of that sum

to convert degrees to radians multiply by pi and divide by one-eighty
to convert radians to degrees multiply by one-eighty and divide by pi

scalene triangles have no equal sides
isosceles triangles have two equal sides
equilateral triangles have all equal sides

acute angles are less than 90 degrees
obtuse angles are more than 90 degrees
right angles are exactly 90 degrees

the total degrees of interior angles in a polygon with "N" sides
is "N" subtracted by 2 in parentheses times one-eighty

supplementary angles add to one-eighty degrees
circles are congruent if they have the same radii, diameters, circumference and or area
an arc is a segment of the circumference of a circle
a chord is a line connecting two points on the circumference of a circle

In a circle,
a tangent and radius touch at a 90 degree angle
In a circle,
when an inscribed angle makes a semicircle, it is a 90 degree angle.
In a circle,
when two inscribed angles make the same arc, the angles are congruent.
In a circle,
When a quadrilateral is inscribed, opposite angles are supplementary.
In a circle,
when central angles are congruent, arcs and chords are congruent as well.
In a circle,
the length of an arc is the circumference times the degrees divided by three-sixty

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the equation for a line is "y" equals "m" times "x" plus "b" where "m" is the slope and "b" is the "y" intercept the slope is the change in "y" over the change in "x" if "m" equals "m", two lines are parallel if "m" equals negative one divided by "m", two lines are perpendicular congruent means to have the same size or shape pi is approximately three point one four the diameter of a circle is the radius times two the circumference of a circle is pi times the diameter a parallelogram has 4 sides (Quadrilateral) opposite sides are parallel pairs of opposite sides and angles are congruent The rhombus, rectangle, and square are all parallelograms the perimeter of a rectangle is 2 times length plus 2 times width the perimeter of a square is 4 times side length the area of a square is side length squared the area of a rectangle is length times width the area of a parallelogram is length times height the area of a triangle is base times height divided by two the area of a circle is pi times radius squared the volume of a sphere is four-thirds times pi times radius to the third the volume of a cylinder is height times pi times radius squared the volume of a cone is one-third times pi times radius to the third the volume of a pyramid is base area times height divided by three the volume of a cube is side length to the third the volume of a prism is base area times height sine is opposite over hypotenuse cosine is adjacent over hypotenuse tangent is opposite over adjacent secant is 1 over the cosine cosecant is 1 over the sine cotangent is 1 over the tangent The Law of Sines is sine of Alpha over "A" equals sine of Beta over "b" equals sine of Gamma over "c" where Alpha, Beta, and Gamma are the angles of the triangle and "A", "b", and "c" are the sides opposite those angles The Law of Cosines is "c" squared equals "A" squared plus "b" squared minus two times "A" times "b" times cosine of Gamma where "c" is the length of the side opposite Gamma, "A" and "b" are the lengths of the other two sides, and Gamma is the angle between sides "A" and "b". Pythagorean Theorem is "A" squared plus "b" squared equals "c" squared To get distance, take the change in "x" squared and add it to the change in "y" squared then take the square root of that sum to convert degrees to radians multiply by pi and divide by one-eighty to convert radians to degrees multiply by one-eighty and divide by pi scalene triangles have no equal sides isosceles triangles have two equal sides equilateral triangles have all equal sides acute angles are less than 90 degrees obtuse angles are more than 90 degrees right angles are exactly 90 degrees the total degrees of interior angles in a polygon with "N" sides is "N" subtracted by 2 in parentheses times one-eighty supplementary angles add to one-eighty degrees circles are congruent if they have the same radii, diameters, circumference and or area an arc is a segment of the circumference of a circle a chord is a line connecting two points on the circumference of a circle In a circle, a tangent and radius touch at a 90 degree angle In a circle, when an inscribed angle makes a semicircle, it is a 90 degree angle. In a circle, when two inscribed angles make the same arc, the angles are congruent. In a circle, When a quadrilateral is inscribed, opposite angles are supplementary. In a circle, when central angles are congruent, arcs and chords are congruent as well. In a circle, the length of an arc is the circumference times the degrees divided by three-sixty [End]

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