Math for 800 11 quadrilaterals, circles and polygons
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Transcript of Math for 800 11 quadrilaterals, circles and polygons
![Page 1: Math for 800 11 quadrilaterals, circles and polygons](https://reader034.fdocuments.net/reader034/viewer/2022052401/55b7e398bb61eb1d198b4641/html5/thumbnails/1.jpg)
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www.twitter.com/mathfor800
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WHAT IS A QUADRILATRAL?
Any four-sided figure.
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SUM OF THE INTERIOR ANGLES
The interior
angles of any
quadrilateral
sum up to 360o.
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PARALLELOGRAM
Is a quadrilateral
with two opposite
and equal pairs of
sides (square,
rectangle, rhombus).
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PARALLELOGRAM
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PERIMETER OF A PARALLELOGRAM
Is the sum of
all the sides.
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AREA OF A PARALLELOGRAM
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PROP. OF PARALLELOGRAM
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x
x
d2
4Perimeter x
Area x
SQUARE
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SQUARE
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D1
D2
x
x
1 2
4
1
2
Perimeter x
Area D D
RHOMBUS
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RHOMBUS
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RHOMBUS
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x
y
x
y
2 2Perimeter x y
Area x y
RECTANGLE
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RECTANGLE
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RECTANGLE
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TRAPEZOID
h
b2
b1
1 2
1
2Area b b h
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AREA OF STRANGE
QUADRILATERALS
x
y
A
B
C
D
(5, 0)
(3, 4)
(1, 0)
(6, 5)
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AREA OF STRANGE
QUADRILATERALS
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QUADRILATERALS
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CIRCLE
Any three point in a
plane, not on the
same line, uniquely
define a circle.
A
r
CB
O
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RADIUS
A radius (OT) goes
from the center of a
circle to its
circumference
(perimeter).
OA B
R
Q
T
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DIAMETER
A diameter (AB)
connects two points
on the circumference
of the circle, going
through the center.
A diameter is equal to
two radii.
OA B
R
Q
T
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CHORD
A chord (RQ)
connects two points
on the
circumference of
the circle.
OA B
R
Q
T
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TANGENT
A line (t) that touches
only one point on the
circumference of the
circle and is
perpendicular to the
radius at that point.
O B
T
t
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SECANT
A line (CD) that
intersects two points
on the curve.O B
T
tC
D
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ARC
An arc (TB) is a portion
of the circumference
of a circle.
C
D
T
B
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CENTRAL ANGLE
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CENTRAL ANGLE
The degree
measure of a
central angle is the
same as the
degree measure of
its intercepted arc.
A
BO
90oAB
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A
C40°
80oAC
INSCRIBED ANGLE
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A
C40°
80oAC
INSCRIBED ANGLE
The degree
measure of an
inscribed angle is
half the degree
measure of its
intercepted arc.
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ANGLE INSCRIBED IN A SEMICIRCLE
B
CA
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CENTRAL AND INSCRIBED ANGLES
A
C
O
B
80oAC
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CIRCUMFERENCE
Is the
perimeter of a
circle.
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2C r
C d
CIRCUMFERENCE
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l
O
2360
l r
LENGTH OF ARC
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AREA OF THE CIRCLE
Is the number
of square
units inside
that circle.
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2
2
4
A r
dA
AREA OF THE CIRCLE
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A fraction of the circle.
As
2Area=360
r
AREA OF A SECTOR
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CIRCLES
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POLYGONS
2-dimensional
shapes. They are
made of straight
lines, and the
shape is "closed"
(all the lines
connect up).
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MAIN ELEMENTS IN A POLYGON
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REGULAR POLYGON
A polygon
with all equal
sides and all
equal
angles.
Regular polygons are always convex.
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The sum of
the lengths
of all the
sides.
PERIMETER OF A REGULAR POLYGON
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APOTHEM
The apothem of
a regular
polygon is
perpendicular to
a side, bisects
that side, and
also bisects a
central angle.
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1
2Area apothem perimeter
AREA OF A REGULAR POLYGON
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ANGLES IN A POLYGON
x: Interior angle
y:Exterior angle
z: Central anglez
x y
O
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ANGLES IN A POLYGON
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2 180n
n: number of sides
SUM OF THE INTERIOR ANGLE MEASURES
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2 180n
n
n: number of sides
INTERIOR ANGLE MEASURE
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360
n
n: number of sides
EXTERIOR/CENTRAL ANGLE MEASURE
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POLYGONS
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INSCRIBED FIGURES
A polygon is
inscribed in a
circle if all the
vertices of the
polygon lie with
the circle.
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CIRCUMSCRIBED FIGURES
A polygon is
circumscribed
about a circle if all
the sides of the
polygon are
tangent to the
circle.
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SHADED AREAS
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SHADED AREAS
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MULTIPLE FIGURES
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SUMMARY
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MATH FOR 800
GRE - GMAT
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