Geometry Flashcards
Slope of a line
Upwards: positive
Downwards: negative
Horizontal: 0
Vertical: undefined
Inscribed vs central
central angle is twice the inscribed angle
Inscribed: vertex at the circle
Inscribed triangle
All vertices are points on the circle
*if one of the sides of an inscribed triangle is a diameter, triangle must be right and splits circle in half
Triangle sides
Side - side < X < side + side
Isosceles triangle
Sides
Angle
Property relating to a square
X, X, X rt 2
45-45-90
Half a square, can use to find length
Equilateral
Sides, angles
Property relating to 30-60-90 triangle
Height
All sides and angles equal
Sides: X, 2X, X rt 3
Height
A * rt 3
——-
2
2 30-60-90 triangles
Diagonal of square
S sq rt 2
Diagonal of a rectangle
Root of (a squared) + ( b squared)
Sphere
Area
Volume
volume: 4 pi r^3
——–
3
SA: 4 pi r^2
Circles
Circumference Diameter Radius Area Perimeter of sector
Circumference: 2 pi r
Area
Parallelogram properties
- Opposite sides and angles equal
- Consecutive angles supplementary
- If one angle is right, all are right
- Diagonals bisect each other
- Angles total to 360
- Diagonals separates it into 2 equal triangles
- Opposite sides parallel
*note: parallel lines doesnt ahtomatically mean that they are equal in length
Volume
Cube Rectangular prism Cylinder Cone Pyramid Sphere
Cube - side ^ 3
Rectangular prism - length x breadth x height
Cylinder - pi * r squared * h
Cone - 1/3 of cylinder
Pyramid - 1/3 base length * based width * base height
Sphere - 4/3 pi r ^3
Area of rhombus
(Diag 1 * diag 2) / 2
Diagonals of square vs rhombus
Diagonals of square and rectangle
Square and rhombus: perpendicular bisectors
Square and rectangle:
equal length
Sum of interior angles of polygon
180* n-2
