Geometry Flashcards
Angles less than 90
Acute Angles
Angles between 90 - 180
Obtuse Angles
Sum of all interior angles of pentagon =
540
Sum of all interior angles of hexagon =
720
Formula for sum of all interior angles of a shape
= ( n - 2 ) x 180
Corner of a polygon is called
Vertex
Area of Trapezoid
(Base1 + Base 2) x Height / 2
or
Average of two bases x Height
The side of the triangle opposite to the largest angle.
Hypotenuse
Pythagorean Theorem
a^2 + b^2 = c^2
Common right triangles’ sides:
3-4-5
5-12-13
8-15-17
Ratio of lenghts of sides of a 45-45-90 triangle
x : x : x√2
Ratio of lengths of sides of a 30-60-90 triangle
x, 2x, x√3
An exterior angle of a triangle is equal to
the sum of two non-adjacent (opposite) interior angles of the triangle.
Area of Triangle
Base x Height / 2
Any line segment that connects two points on a circle
Chord
Formula for circumference
C = π x d
Area of a circle
A = π r^2
Angle whose vertex lies at the center point of a circle.
Central Angle
Angle that has its vertex on the circle itself.
Inscribed Angle
An inscribed angle is equal to
Half of the arc it intercepts
Volume of cylinder
V = π r^2 h
Quadrant Numbers
I (+,+)
II (-,+)
III (-,-)
IV (+,-)
Formula for slope
rise/run
Ysub2 - Ysub1
/
Xsub2 - Xsub1
Kinds of slope
Positive: rises from left to right
Negative: falls from left to right
Zero slope: horizontal
Undefined slope: vertical
A point where a line intersects a coordinate axis
Intercept
Formula for Linear Equation
y = mx + b
Area of Rhombus
Diagonal 1 x Diagonal 2 / 2
Quadrilateral with the biggest area
Square
Quadrilateral with the smallest perimeter (though same area)
Square
If you are given two sides of a triangle or parallelogram, how to maximize area?
Place the two sides perpendicular to each other.
Area of an equilateral triangle 60-60-60 (in terms of side)
S^2 √ 3
/
4
Ratio of area of two similar triangles with side length ratio of a:b
a^2 : b^2
Formula for diagonal of a square
d = s x √2
Formula for diagonal of a cube
d = s x √3
Surface area of a cyclinder
= 2 (π r^2) + 2 π r h
How to find equation of perpendicular bisector
- Find the negative reciprocal slope
- Find the midpoint of the two points by computing the average
- Plug into formula y = mx + b
Parabola curve opens upward means value for A is
Positive
Parabola curve opens downward means value for A is
Negative
Parabola curve is narrow means | A | is
Large
Parabola curve is wide means | A | is
Small
Graph of a quadratic equation if b^2 - 4ac > 0
Intercepts y below origin
Graph of a quadratic equation if b^2 - 4ac = 0
Intercepts at 0
Graph of a quadratic equation if b^2 - 4ac < 0
Intercepts y above origin
Deluxe Pythagorean Theorem for Rectangular Solids
d^2 = x^2 + y^2 + z^2
where x, y, and z are sides of the rectangular solid and d is the diagonal
Regular Figures where you only need one measurement to know all other
Squares Equilaterals Circles Spheres Cubes 45-45-90 Triangles 30-60-90 Triangles
