Math for 800 11 quadrilaterals, circles and polygons

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WHAT IS A QUADRILATRAL?

Any four-sided figure.

SUM OF THE INTERIOR ANGLES

The interior

angles of any

quadrilateral

sum up to 360o.

PARALLELOGRAM

Is a quadrilateral

with two opposite

and equal pairs of

sides (square,

rectangle, rhombus).

PARALLELOGRAM

PERIMETER OF A PARALLELOGRAM

Is the sum of

all the sides.

AREA OF A PARALLELOGRAM

PROP. OF PARALLELOGRAM

x

x

d2

4Perimeter x

Area x

SQUARE

SQUARE

D1

D2

x

x

1 2

4

1

2

Perimeter x

Area D D

RHOMBUS

RHOMBUS

RHOMBUS

x

y

x

y

2 2Perimeter x y

Area x y

RECTANGLE

RECTANGLE

RECTANGLE

TRAPEZOID

h

b2

b1

1 2

1

2Area b b h

AREA OF STRANGE

QUADRILATERALS

x

y

A

B

C

D

(5, 0)

(3, 4)

(1, 0)

(6, 5)

AREA OF STRANGE

QUADRILATERALS

QUADRILATERALS

CIRCLE

Any three point in a

plane, not on the

same line, uniquely

define a circle.

A

r

CB

O

RADIUS

A radius (OT) goes

from the center of a

circle to its

circumference

(perimeter).

OA B

R

Q

T

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

CHORD

A chord (RQ)

connects two points

on the

circumference of

the circle.

OA B

R

Q

T

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

SECANT

A line (CD) that

intersects two points

on the curve.O B

T

tC

D

ARC

An arc (TB) is a portion

of the circumference

of a circle.

C

D

T

B

CENTRAL ANGLE

CENTRAL ANGLE

The degree

measure of a

central angle is the

same as the

degree measure of

its intercepted arc.

A

BO

90oAB

A

C40°

80oAC

INSCRIBED ANGLE

A

C40°

80oAC

INSCRIBED ANGLE

The degree

measure of an

inscribed angle is

half the degree

measure of its

intercepted arc.

ANGLE INSCRIBED IN A SEMICIRCLE

B

CA

CENTRAL AND INSCRIBED ANGLES

A

C

O

B

80oAC

CIRCUMFERENCE

Is the

perimeter of a

circle.

2C r

C d

CIRCUMFERENCE

l

O

2360

l r

LENGTH OF ARC

AREA OF THE CIRCLE

Is the number

of square

units inside

that circle.

2

2

4

A r

dA

AREA OF THE CIRCLE

A fraction of the circle.

As

2Area=360

r

AREA OF A SECTOR

CIRCLES

POLYGONS

2-dimensional

shapes. They are

made of straight

lines, and the

shape is "closed"

(all the lines

connect up).

MAIN ELEMENTS IN A POLYGON

REGULAR POLYGON

A polygon

with all equal

sides and all

equal

angles.

Regular polygons are always convex.

The sum of

the lengths

of all the

sides.

PERIMETER OF A REGULAR POLYGON

APOTHEM

The apothem of

a regular

polygon is

perpendicular to

a side, bisects

that side, and

also bisects a

central angle.

1

2Area apothem perimeter

AREA OF A REGULAR POLYGON

ANGLES IN A POLYGON

x: Interior angle

y:Exterior angle

z: Central anglez

x y

O

ANGLES IN A POLYGON

2 180n

n: number of sides

SUM OF THE INTERIOR ANGLE MEASURES

2 180n

n

n: number of sides

INTERIOR ANGLE MEASURE

360

n

n: number of sides

EXTERIOR/CENTRAL ANGLE MEASURE

POLYGONS

INSCRIBED FIGURES

A polygon is

inscribed in a

circle if all the

vertices of the

polygon lie with

the circle.

CIRCUMSCRIBED FIGURES

A polygon is

circumscribed

about a circle if all

the sides of the

polygon are

tangent to the

circle.

SHADED AREAS

SHADED AREAS

MULTIPLE FIGURES

SUMMARY

MATH FOR 800

GRE - GMAT

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