Geometry Flashcards
The sum of any two lengths of a triangle will always be _____ than 60*the third side.
greater than
How to find the third same of triangle (largest and smallest)
Largest = Side 1 + Side 2 Smallest = Side 2 - Side 1, where Side 2 is bigger
Smallest
Isosceles triangle
Two equal sides and two equal angles
Equilateral triangle
Three equal sides and all angles equal 60°
Area of a triangle
1/2 base * height
Pythagorean theorem
a^2 + b^2 = c^2 for right triangles only
Common combinations for Pythagorean theorem
3-4-5 5-12-13 6-8-10 8-15-17 9-12-15 12-16-20 10-24-26
Properties of isosceles right triangle
90° - 45° - 45° (hypotenuse - leg - leg)
x*sqrt(2) - x - x
sqrt(2) - 1 - 1
30 - 60 - 90 triangle
30° - 60°- 90°
short - long - hypotenuse
1 - sqrt(3) - 2
x - x*sqrt(3) - 2x
What do you get when you put two 30-60-90 triangles together by their long sides?
An equilateral triangle
Trapezoid
4 sides - one pair parallel
Parallelogram
4 side - opposite sides and opposite angles equal
slanted rectangle
Rectangle
4 sides - all angles are 90° and opposite sides are equal
Square
4 sides - all angles are 90° and all sides are equal.
Rhombus
4 sides -opposite sides and opposite sides are equal. All sides are equal.
(slanted square)
How to find the sum of the interior angles of a shape
(n-2)*180
triangle = 180 square/rectangle = 360 pentagon = 540 hexagon = 720
Area of a Trapezoid
(Base 1 + Base 2)/2 x height
Area of any parallelogram
base x height
For all quadrilaterals, how can you maximize area?
make it into a square
For all quadrilaterals, how can you minimize perimeter?
make it into a square
A regular polygon with all sides equal and all angles equal will what?
maximize area for a given perimeter and minimize perimeter for a give area.
If you are given two sides of a triangle or parallelogram, you can do what?
maximize the area by placing those two sides perpendicular to each other.
Circumference of a circle
C = 2pi*r
Area of a circle
A = pi*r^2
What is a sector?
A fractional portion of a circle
What is an inscribed angle?
An angle that has its vertex on the circle itself
An inscribed angle is equal to what?
1/2 the central angle ( or arc) it intercepts
If one side of an inscribed triangle is a diameter of the circle then it must be what?
It must be a right triangle
Surface area of a cylinder
SA = 2 (pir^2) +2pirh
Volume of a cylinder
V = pi*r^2h
Sum of the interior angles formed by intersecting lines of a circle
360*
Supplemental angles
sum to 180*
An exterior angle of a triangle is equal to what?
An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
Quadrants of a plane
(Counterclockwise) I, II, III, IV
Equation for a line
y = mx +b
slope
rise/run = change in y/change in x
x-intercept
where y=0
y-intercept
where x=0
