Upload
uma
View
53
Download
0
Embed Size (px)
DESCRIPTION
Please make a new notebook. It’s for Chapter 6/Unit 3 Properties of Quadrilaterals and Polygons. Then, would someone hand out papers, please? Thanks. ♥. to Unit 3 Properties of Quadrilaterals. Chapter 6 Polygons a n d Quadrilaterals. Please get: 6 pieces of patty paper protractor - PowerPoint PPT Presentation
Citation preview
Please make a new notebook
It’s for Chapter 6/Unit 3Properties of
Quadrilaterals and Polygons
Then, would someone hand out papers, please? Thanks.♥
Chapter 6 Polygons and Quadrilaterals
to Unit 3
Properties of
Quadrilateral
s
Please get:•6 pieces of patty paper•protractor•Your pencil
But first
…
Let’s define ‘polygon’
The word ‘polygon’
is a Greek word.Poly means many and
gon means angles
What else do you know about a
polygon?
In this activity, we are going explore the interior and exterior angle measures of polygons.
Let’s define ‘polygon’
The word ‘polygon’
is a Greek word.Poly means many and
gon means angles
What else do you know about
a polygon?
♥A two dimensional object♥A closed figure♥Made up of three or more straight line segments♥There are exactly two endpoints that meet at a vertex♥The sides do not cross each other
There are also different types of polygons:
Convex polygons have interior angles less than 180◦
convex
concave
Concave polygons have at least one interior angle greater than 180◦
K1L1 M1
N1 O1 P1
Q1 R1 S1
Let’s practice:
•Decide if the figure is a polygon. •If so, tell if it’s convex or concave. •If it’s not, tell why not.
Ok, now where were
we?
and the interior and exterior
angle measures.
Oh, yes, an activity about
polygons...
1.
Draw a large scalene acute triangle on a piece of patty paper.Label the angles INSIDE the triangle as a, b, and c.
2.
On another piece of PP, draw a line with your straightedge and put a point toward the middle of the line.
Place the point over the vertex of angle a and line up one of the rays of the angle with the line. 3
.
4.
Trace angle a onto the second patty paper.
5.
Trace angles b and c so that angle b shares one side with angle a and the other side with angle c.
Should look like this:
What did you
just prove about
the interior angle
measures of a
triangle?
Yep. They equal 180◦
1.
2.
3.
4.
5.
Draw a quadrilateral on another PP. Label the angles a, b , c, and d.
Draw a point near the center of a second PP and fold a line through the point.
Place the point over the vertex of angle a and line up one of the rays on the angle with the line. Trace angle a onto the second PP.
Trace angle b onto the second PP so that a and b are sharing the vertex and a side
Repeat with angles c and d.
What did you
just prove about
the interior angle
measures of a
quadrilateral?
Yep. They equal 360◦
Tres mas…
1.
2.
Repeat these steps for a pentagon.Remember to figure the sum of the interior angles.
Repeat these steps for a hexagon.Remember to figure the sum of the interior angles.
Number of sides of the polygon
3 4 5 6 7 8
Sum of the interior angle measures
Can you find the pattern?Can you
create an
equation for the pattern?Put this table in your notes and complete it:
180 360 540 720 900 1080
Behold…
total sum of the interior
angles of a polygon
(The number of sides
of a polygon – 2)(180)
(n – 2)(180)
=
Or, as we mathematicians prefer to say…
QuadrilateralPentagon
180o 180
o180o
180o
180o
2 x 180o = 360o 3
4 sides5 sides
3 x 180o = 540o
Hexagon6 sides
180o
180o
180o
180o
4 x 180o = 720o
4 Heptagon/Septagon7 sides
180o180o 180o
180o
180o
5 x 180o = 900o 5
2 1 diagonal
2 diagonals
3 diagonals 4 diagonals Polygons
3.
♥On your PP with the triangle, extend each angle out to include the exterior angle.
♥Measure and record each linear pair.
♥What is the total sum of the exterior angles?
♥Do the same with the quadrilateral, pentagon and hexagon.
♥Remember to record each linear pair.
♥Can you make a conjecture as to the sum of exterior angles?Number of sides of the polygon
3 4 5 6 7 8
Sum of the interior angle measures
180 360 540 720 900 1080
Sum of the exterior angle measures 360 360 360 360 360 360
TADA!You have just proven two very important theorems:
Polygon Angle-Sum
Theorem (n-2) 180
Polygon Exterior
Angle-Sum TheoremAlways = 360◦
A quick polygon naming lesson:# of sides Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon/Septagon
8 Octagon
9 Nonagon
10 Decagon
12 Dodecagon
n n-gon
I ♥ Julius and Augustus
A regular polygon is equilateraland equiangular
TriangleSquare
Heptagon Octagon Nonagon
Pentagon Hexagon
Dodecagon
Let’s practice:
1. How would you find the total interior angle sum in a convex polygon?
2. How would you find the total exterior angle sum in a convex polygon?
3. What is the sum of the interior angle measures of an 11-gon?
4. What is the sum of the measure of the exterior angles of a 15-gon?
5. Find the measure of an interior angle and an exterior angle of a hexa-dexa-super-double-triple-gon.
6. Find the measure of an exterior angle of a pentagon.
7. The sum of the interior angle measures of a polygon with n sides is 2880. Find n.
(n-2)(180)
The total exterior angle sum is always 360◦
1620◦
360◦
180◦
360/5 = 72 ◦
2880 = (n-2)(180)n = 18 sides
Assignment
pg 3567 – 27,29-3540-41,49-54