Geometry Flashcards
Ratio of sides for a 45-45-90 triangle?
X : X : X(sq rt 2)
3 common Pythagorean triples
3 - 4 - 5
5 - 12 - 13
8 - 15 - 17
Ratio of sides for 30-60-90 triangle
30 - x
60 - x (sq rt 3)
90 - 2x
Area of triangle
1/2(base) x height
Area of trapezoid
(Base1 + Base2) / 2 x height
Area of a circle
pie (radius^2)
How do you find slope of a line?
Rise/run or change in y over change in x. Need 2 point (x1,y1) (x2,y2)
Equation for a line in slope - intercept form
Y =mx + b
M = slope B = y-intercept (where x=0)
Area of parallelogram
Base x height
Circumference of a circle
pie (diameter)
2r (pie)
Slope and slope of perpendicular line
Slope = m
Perpendicular slope = (- 1/m)
Two sides of a triangle are 4 and 10. If the third side is an integer x. How many possible values are there for x?
X must be greater than 10-4 and less than 10 + 4
So 7,8,9,10,11,12,13
Deluxe Pythagorean theorem
D^2= x^2 + y^2 + z^2 where x, y and z are the sides of a rectangular solid and d is the main diagonal.
What defines similar triangles?
If corresponding angles are equal and corresponding sides are in proportion.
Once you find 2 triangles and 2 pairs of equal angles = similar
Area of equilateral triangle with side length S=
(S^2)(sq rt 3) / 4
Diagonal of a square with side length s
S(sq rt 2)
Diagonal of cube with edge length s
S(sq rt 3)
What is an inscribed angle in a circle? VS. central angle
An inscribed angle has it’s vertex on the line of the circle.
A central angle’s vertex lies at the center point of a circle.
An inscribed angle is 1/2 the arc it intercepts
Proof needed to show that quadrilateral is a square
1) diagonals bisect each other
2) one right angle
Definition of parallelogram
Opposite sides =
Opposite angles =
Definition of rectangle
All angles = 90
Opposite sides equal
- a rectangle is a special type of parallelogram
- a square is a special type of rectangle
Definition of rhombus
All sides =
Opposite angles are equal
- rhombus is a special type of parallelogram
- square is a type of rhombus
Volume of cylinder
Pie (r^2)(h)
What is isosceles triangle?
Triangle in which 2 sides are equal
45-45-90
X-X-X(sq rt 2)
Distance between 2 points (x1,y1) and (x2,y2)
-2,9) and (-7,-3
Sq rt ( (x-x)^2 + (y-y)^2)
13
Surface area of a cylinder
2(pie)r^2 + 2(pie)rh
R- radius
H- height
Volume of cylinder
(Pie)(r^2)(h)
Perpendicular slopes
2 lines that are perpendicular have slopes that are negative reciprocal i.e. when product of slopes is -1
A quadrilateral has a perimeter of 36 inches.
What shape results in maximum area?
Minimum area?
9 x 9 square has max area
1 x 17 rectangle has min area
Given a fixed area value, what shape has minimum perimeter?
Square had minimum perimeter (or other polygon w/ right angles)
Given two sides of a triangle or parallelogram, how do you maximize area?
Place sides perpendicular
Proof needed for similar triangles
2 angles equal.
Similar triangles have all angles equal and all angles in proportion.
Relationship btw side lengths and areas of similar triangles
If sides are in ratio of a:b then their areas will be in ratio of a^2:b^2
Circ of a circle
2(pie)(r)
