Welcome! Please go get your interactive notebook. Please read the board.
Please make a new notebook
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Transcript of Please make a new notebook
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Please make a new notebook
It’s for Chapter 6/Unit 3Properties of
Quadrilaterals and Polygons
Then, would someone hand out papers, please? Thanks.♥
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Chapter 6 Polygons and Quadrilaterals
to Unit 3
Properties of
Quadrilateral
s
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Please get:•6 pieces of patty paper•protractor•Your pencil
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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.
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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
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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◦
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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.
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Ok, now where were
we?
and the interior and exterior
angle measures.
Oh, yes, an activity about
polygons...
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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:
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What did you
just prove about
the interior angle
measures of a
triangle?
Yep. They equal 180◦
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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.
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What did you
just prove about
the interior angle
measures of a
quadrilateral?
Yep. They equal 360◦
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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
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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…
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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
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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
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TADA!You have just proven two very important theorems:
Polygon Angle-Sum
Theorem (n-2) 180
Polygon Exterior
Angle-Sum TheoremAlways = 360◦
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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
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A regular polygon is equilateraland equiangular
TriangleSquare
Heptagon Octagon Nonagon
Pentagon Hexagon
Dodecagon
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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
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Assignment
pg 3567 – 27,29-3540-41,49-54