1. POLYGONS
10/17/2007
NAMING
POLYGONS
EQ: How do I find the measure of an interior & exterior angle of a polygon?

2. What does the word “polygon” mean?
10/17/2007
POLYGONS
Let's Discuss
What does the word “polygon” mean?
What is the smallest number of sides a polygon can have?
What is the largest number of sides a polygon can have?
EQ: How do I find the measure of an interior & exterior angle of a polygon?

3. Triangle Octagon Quadrilateral Nonagon Pentagon Decagon Dodecagon
POLYGONS
10/17/2007
Triangle
Octagon
Quadrilateral
Nonagon
Pentagon
Decagon
Dodecagon
Hexagon
n-gon
Heptagon
EQ: How do I find the measure of an interior & exterior angle of a polygon?

4. Important Terms A VERTEX is the point of intersection of two sides F A
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POLYGONS
Important Terms
A VERTEX is the point of intersection of two sides
CONSECUTIVE VERTICES are two endpoints of any side. F A B C D E
A segment whose endpoints are two
nonconsecutive vertices is called a DIAGONAL.
Sides that share a vertex are called CONSECUTIVE SIDES.
EQ: How do I find the measure of an interior & exterior angle of a polygon?

5. More Important Terms EQUILATERAL - All sides are congruent
10/17/2007
POLYGONS
More Important Terms
EQUILATERAL - All sides are congruent
EQUIANGULAR - All angles are congruent
REGULAR - All sides and angles are congruent
EQ: How do I find the measure of an interior & exterior angle of a polygon?

6. Diagonals & Angle Measures 10/17/2007
POLYGONS
10/17/2007
Diagonals &
Angle Measures
EQ: How do I find the measure of an interior & exterior angle of a polygon?

7. What is the sum of the measures of the interior angles of a triangle?
REVIEW:
POLYGONS
10/17/2007
What is the sum of the measures of the interior angles of a triangle?
180°
180°
180°
What is the sum of the measures of the interior angles of any quadrilateral?
360°
EQ: How do I find the measure of an interior & exterior angle of a polygon?

8. POLYGONS
10/17/2007
If a convex polygon has n sides, then the sum of the measure of the interior angles is (n-2)(180°)
EQ: How do I find the measure of an interior & exterior angle of a polygon?

9. Ex. 1 Use the regular pentagon to answer the questions.
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POLYGONS
Ex. 1 Use the regular pentagon to answer the questions.
Find the sum of the measures of the interior angles.
Find the measure of ONE interior angle
540°
108°
EQ: How do I find the measure of an interior & exterior angle of a polygon?

10. Two more important terms
POLYGONS
10/17/2007
Two more important terms
Interior Angles
Exterior Angles
EQ: How do I find the measure of an interior & exterior angle of a polygon?

11. 10/17/2007
POLYGONS 1 2 3 4 5
If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°.
EQ: How do I find the measure of an interior & exterior angle of a polygon?

12. 10/17/2007
POLYGONS
If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 3 2
EQ: How do I find the measure of an interior & exterior angle of a polygon?

13. Ex. 2 Find the measure of ONE exterior angle of a regular hexagon.
POLYGONS
10/17/2007
Ex. 2 Find the measure of ONE exterior angle of a regular hexagon.
60°
EQ: How do I find the measure of an interior & exterior angle of a polygon?

14. Ex. 3 Find the measure of ONE exterior angle of a regular heptagon.
POLYGONS
10/17/2007
Ex. 3 Find the measure of ONE exterior angle of a regular heptagon.
51.4°
EQ: How do I find the measure of an interior & exterior angle of a polygon?

15. Ex. 4 The sum of the measures of five interior angles of a hexagon is What is the measure of the sixth angle?
POLYGONS
10/17/2007
185°
EQ: How do I find the measure of an interior & exterior angle of a polygon?

16. Ex. 5 The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle.
POLYGONS
10/17/2007
30°, 90°, 150°, and 30°
EQ: How do I find the measure of an interior & exterior angle of a polygon?

17. Ex. 6 The sum of the interior angles of a polygon is 720
Ex. 6 The sum of the interior angles of a polygon is Find the number of sides.
POLYGONS
10/17/2007
n = 6
EQ: How do I find the measure of an interior & exterior angle of a polygon?

18. POLYGONS
10/17/2007
Homework:
Page 300 # 1-21
EQ: How do I find the measure of an interior & exterior angle of a polygon?