Section 5.4: Four Sided

Polygons

By Joe Lenahan

Polygons- closed plane figure made up of several line segments that are joined together. The sides do not cross each other. Exactly two sides meet at every vertex.

These are examplesof polygons

Polygons

Polygons

JOEL is not a polygon because a polygon consists entirely of segments

J

O E

L

P

R I

C

YPRICY is not a polygon. In a polygon, consecutive sides intersect only at endpoints. Nonconsecutive sides do not intersect

Naming PolygonsYou name polygons by starting at any vertex

and then proceeding either clockwise or counter clockwise

A

B C

D

If you start at A, the polygon would be called either ABCD or ADCB

Convex Polygon

Convex polygon- Every interior angle is less than 180o

These are all convex polygons

Convex Polygons

L

M

O

N

P

LMNOP is not convex because P is greater then 180. LMNOP is a concave figure which is a figure in which at least one interior angle is more than 180

Diagonals of Polygons

Diagonal- any segment that connects two nonconsecutive vertices of a polygon

A

B

C

D E

F

G

H

In polygon ABCDEFGH, CH and AF are diagonals

Quadrilaterals

QuadrilateralQuadrilateral- four sided polygon

Special Quadrilaterals

Parallelogram- quadrilateral in which both pairs of opposite sides are parallel and congruent

Rectangle- a parallelogram in which at least one angle is right

Rhombus

-a parallelogram in which at least two consecutive sides are congruent

Square- a parallelogram that is both a rhombus and

a square

More Special Quadrilaterals

Kite- a quadrilateral in which two disjoint pairs of consecutive sides are congruent

Trapezoid- a quadrilateral only have one pair of parallel sides, the bases

IsoscelesTrapezoid

- a trapezoid in which the non-parallel

sides are congruent

Sample Problems

Is this a polygon?

The answer is no because a circle doesn’t have any sides or vertices

F L

N X

Starting at point F, what would the name of this polygon be?

FLXN or FNXL

More Sample Problems

Give the most descriptive names for the following shapes:

congruent

congruent

The most descriptive name is rectangle

The most descriptive name is parallelogram

x3

3xy

x4 2x-1

1)

Find x and y if ABCD is a rectangle.

A

B C

D

Practice Problems

Practice Problems Continued

Always, Sometimes, Never– A trapezoid is a parallelogram– A square is a rhombus– A polygon is a parallelogram– An isosceles trapezoid is a polygon– A square is an isosceles trapezoid– A parallelogram is a rectangle

2)

Practice Problems Cont’

Name this polygon, stating at point Z and two diagonals

Z

I

O P

X

F

WY

3)

Answers

1) y=7, x=5 2) N,A,S,A,N,S 3) ZYWFXPOI or ZIOPXFXY, and

YP and IX

For Your Enjoyment

Just A Boring Square

Bibliography

"Polygon Properties." Math.Com: the World of Math Online. 2005. Math.Com. 30 May 2008 <http://www.math.com/tables/geometry/polygons.htm>.

Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, Illinois:

McDougal Littell, 1991.