GEOMETRY Flashcards
Volume of a cylinder
Pi r^2 h
Volume of a cylinder: multiplying r and h
Pi x (2r)^2 x 2h
= pi x 4 x r^2 x 2 x h
= 8 pi r^2 h
Sum of all interior angles in a triangle =
180 degrees
Perimeter of triangle =
Sum of all sides
Area of a triangle =
(1/2)(base)(height)
Base and Height of a triangle must ….
Be perpendicular / form a 90 degree angle
Triangle Inequality Theorem
- Any side of a triangle is always shorter than the sum of the other two sides
- Any side of a triangle is always longer than the difference of the other two sides
Isosceles Triangle is…
A triangle in which two sides are equal (so their angles are also equal)
Equilateral triangle
All three sides (and all three angles) are equal
Right Triangle - Pythagorean Theorem
A^2 + b^2 = c^2
THE SQUARE OF THE HYPOTENUSE OF A RIGHT TRIANGLE IS EQUAL TO THE SUM OF THE SQUARE OF THE TWO ADJACENT SIDES
3 x 4 x 5 triangle
5 x 12 x 13 triangle
If you see a right triangle with sides of 3, 4; 4,5; 3,5 (or a multiple of these numbers), you know the other side is one of (a multiple of) 3, 4 or 5
SAME WITH 5 X 12 X 13
ONLY APPLIES TO RIGHT TRIANGLES
45 45 90 TRIANGLE
A right triangle with a 45 degree angle is an isosceles right triangle with one other 45 degree angle
Sides other than the hypotenuse will be equal to x
The hypotenuse will be equal to x root 2
30 60 90 triangle
60 / 30 / 90 degrees
Side opposite 30 degrees is x
Hypotenuse is 2x
Other side is x root 3
Area of a circle
Pi r squared
Circumference of a circle
2 pi r
Diameter of circle
2 r
Degrees in a circle
360
Length of an arc of a circle
The same fraction of the circumference of the circle as the angle made by that arc is to 360
Polygon
Closed plane figure formed by three or more line segments
Perimeter of a polygon
Sum of all sides
Sum of interior angles of a polygon with n sides
(N-2)*180
Parallelograms
Rectangles and squares - quadrilaterals whose opposite sides are parallel
Features of a parallelogram - sides and angles
Opposite sides are equal
Opposite angles are equal
Diagonals bisect
Area of a parallelogram
Area = Base x Height
Trapezoid
Quadrilateral with only one pair of parallel sides
Area of a trapezoid
(Side a + side b)/2 * h
Surface Area for rectangular solids
Sum of the area of all sides
Surface Area for Cylinder
Area of the bases (circles) x 2
PLUS
Base (diameter) x height
Coordinate geometry: equation for a line
Y = mx + b
Where m = slope
And b = y intercept
Equation for slope of a line
(Y1 - y2) / (X1 - x2)
