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Lesson 30 6.1 & 6.2 Angles in Polygons & Parallelograms.notebook

October 24, 2016

6.1 Angles in Polygons Goal: Students will develop and apply the relationships of both interior and exterior angles in polygons with (n) sides What is a polygon??????

Which of these are polygons?

Polygon: A closed figure formed by a finite number of coplanar segments (sides) such that each side intersects two other sides, but only at their endpoints (vertices). 1


October 24, 2016

Polygons are named based on the number of sides that create them: # of sides 3 4 5 6 7 8 9 10 11 12 n

Name Octagon

Heptagon Nonagon Undecagon

Pentagon Triangle

ngon

Quadrilateral Decagon

Hexagon Dodecagon

Polygons are also described as being convex or concave: In a convex polygon all interior angles are less than 1800

In a concave polygon at least one angle is greater than 1800

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October 24, 2016

Polygon Interior Angle Sum Theorem

What is the sum of the interior angles of a triangle?

How about a quadrilateral?

How about this quadrilateral?

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October 24, 2016

Can we use triangles to help us to find a pattern? Draw all of the diagonals from one vertex.

# of sides # of Triangles

Sum of interior angles

n Use this formula to find the sum of the interior angles of each of the following: 1.

2.

3. undecagon

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October 24, 2016

If we can find the sum of the interior angles then how to we find the measure of each interior angle of a regular ngon?

1. Find the measure of one interior angle of a regular octagon.

2. If one interior angle in a regular ngon is 1440, how many sides does it have?

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October 24, 2016

What about the exterior angles?

1

2

5 3

4 Knowing that the sum of all exterior angles of a convex polygon is 3600 what is the measure of each exterior angle of a regular ngon?

What is the sum of the exterior angles of a dodecagon?

What is measure of one exterior angle in a 24gon?

If one exterior angle of a regular ngon is 12 degrees, how many sides does it have?

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October 24, 2016

Summary: Here are the four formulas that we have developed today.

Formula Sheet

Sum of the angles

One angle in a regular ngon

Interior Angles Exterior Angles

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October 24, 2016

Practice: A) Find the measure of each exterior angle of a regular 15 gon.

B) Find the measure of each interior angle of a regular dodecagon.

C) The measure of an interior angle of a regular polygon is 156. Find the number of sides.

D) Find the sum of the of the interior angles of a dodecagon.

E) Find the measures of an exterior angle and an interior angle if the regular polygon has 7 sides.

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October 24, 2016

With your table partners, solve for x and y as well as each angle.

4x+5

7x

9y

2y

139O

6x+10

5x5

4x+10

6y

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October 24, 2016

6.2 Parallelograms Goal Students will be able to recognize the conditions that ensure a quadrilateral is a parallelogram.

parallelogram : a quadrilateral whose opposite sides are parallel.

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October 24, 2016

On your own... 1.

Using a straightedge, draw a triangle.

2.

Using patty paper trace your triangle and rotate it so it is next to your original triangle.

3.

What do you notice?

4.

Now trace the other triangle so you have both triangles on one piece of patty paper.

5.

Draw in the other diagonal.

6.

What do you notice about the diagonals?

0

06

0

56

750

0

650

57

600

Properties of Parallelograms:

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October 24, 2016

Ex 1: Solve for x and y 5y 6 3x+4

2x+6

12y 34

Ex 2: Find the measure of: C

B 95

30

A

CED

50

E D

CDA

CDE EDA

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October 24, 2016

Assignment 6.1 - p. 394: 14-20 even, 23-27 odd 32-35 6.2 - p. 403: 9-12, 15-17, 31-34

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