Geometry Flashcards
Hypotenuse = 10
Sides = 6 & 8
Hypotenuse = 15
Sides = 9 & 12
Hypotenuse = 17
Sides = 8 & 15
Hypotenuse = 26
Sides = 10 & 24
Sum of Any Two Sides of a Triangle
> 3rd side
Difference of Any Two Sides of a Triangle
< 3rd Side
Exterior Angle of a Triangle
A = C+D
30-60-90 Triangle
Ratio of Sides
** x : x(3)1/2 : 2x**
1 : (3)1/2 : 2
45-45-90 Triangle
Ratio of Sides
x : x: x(2)1/2
1 : 1 : (2)1/2
Sum of interior angles in a polygon with n sides
180 (n-2)
Measure of One Interior Angle
Volume of a Sphere
Volume of a Cylinder
Suface Area of a Cylinder
=
2(πr<span>2</span>) + 2(πrh)
Suface Area of a Sphere
=
4πr2
Area of Trapezoid
1/2 (sum of bases)(height)
Isoceles Trapezoid
A trapezoid in which the sides (not the bases) are of equal length
Area of an Equilateral
(shortcut formula )
Optimal use:
Given = one side of the triangle and you are asked to find area from that one side.
Area of Reg. Hexagon
Characteristics of a (regular) Hexagon
- six equal sides
- six equal angles
- Σ interior angles = 720°, each angle 120°
- six equilateral triangles formed by three diagonals
Suplementary Angles
Form a straight line
&
= 180o
Quadrilaterals
Parralellograms, Square, & Rectangles
Characteristics of a Parallelogram
- Opposite angles are equal
- Any two consecutive angles are supplementary (= 180°)
- All rectangles
Area of the Parallelogram
Polygon(s)
A closed 2-D geometric figure composed of only straight lines.
Squares, rectangles, hexagons, rhombuses, etc.
Polygon inscribed in a circle means?
The circle into arcs of equal length
Exterior Angles of Any Polygon
=
360° (when taking one exterior angle at each vertex)
Characteristics of a Square
- considered a “special” rectangle - rectangle with equal sides
- each diagonal divides the square into two equal 45-45-90 degree triangles
- all angles are equal
Length of a Diagonal of a Square
= side * 21/2
“the length of one side times the square root of two”
Suface Area of a Cube
= 6s2
Diagonal of a cube
= s(31/2)
or
“side root three”
Diagonal of a Rectangle
*But remember* diagonals of a rectangle do not auto make
congruent 30-60-90 triangles.
PAY ATTN to the givens!!
Suface Area of Rectangular Solid
= 2(LW) + 2(LH) + 2(WH)
Diagonal of Rectagular Solid
(aka Super Pythagorean Theorem)
d2 = l2 + w2 + h2
Sum of Exterior Angles of any Polygon
= 360o
Comparing two quadrilaterals with the same perimeter. Which quad has the greater area?
Square. Because it’s a “squared” calculation.
A rectangle and square have the same area (fixed area),
which figure has a smaller perimeter?
The “rectangle” with the smallest (min.) perimeter
= a square
Isoceles Triagle
= 2 sides are equal and two angles are equal
Area of an Isosceles Right Triagle
=
(l1+ l2)/2
or
SHORTCUT !
L2/2
If there are two quadrilaterals (a square & and a rectangle)
w/ the same perimeter, which of the two quads will have a larger area?
If the rectangle and square have the same perimeter, there are of the square will ALWAYS be larger.
Why?
Area of a square is a squared measure whereas the area of a rectangle is not.
Equilateral Triangle inscribed in a Circle
- Triangle divides the the circle into three equal arcs
- Center if the equilateral triangle = center of circle
Area of the shaded region
=
(area of entire figure) - (area of unshaded region)
Perimeter of Shaded Region
=
(perimeter of entire region) + (perimeter of unshaded region)
Area of circular ring
=
π [(radius2)2 - (radius1)2]
