1. 7-7
Polygons
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Course 1
7-7
Polygons
Learn to identify regular and not regular polygons and to find the angle measures of regular polygons.

3. Insert Lesson Title Here
Course 1
7-7
Polygons
Insert Lesson Title Here
Vocabulary
polygon
regular polygon

4. Course 1
7-7
Polygons
Triangles and quadrilaterals are examples of polygons. A polygon is a closed plane figure formed by three or more line segments. A regular polygon is a polygon in which all sides are congruent and all angles are congruent.
Polygons are named by the number of their sides and angles.

5. Course 1
7-7
Polygons

6. Additional Example 1A: Identifying Polygons
Course 1
7-7
Polygons
Additional Example 1A: Identifying Polygons
Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. A.
The shape is a closed plane figure formed by three or more line segments.
polygon
There are five sides and five angles.
pentagon
All 5 sides do not appear to be congruent.
Not regular

7. Additional Example 1B: Identifying Polygons
Course 1
7-7
Polygons
Additional Example 1B: Identifying Polygons
Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. B.
The shape is a closed plane figure formed by three or more line segments.
polygon
There are eight sides and eight angles.
octagon
The sides and angles appear to be congruent.
regular

8. 7-7 Polygons Try This: Example 1A
Course 1
7-7
Polygons
Try This: Example 1A
Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. A.
There are four sides and four angles.
quadrilateral
The sides and angles appear to be congruent.
regular

9. 7-7 Polygons Try This: Example 1B
Course 1
7-7
Polygons
Try This: Example 1B
Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. B.
There are four sides and four angles.
quadrilateral
The sides and angles appear to be congruent.
regular

10. Course 1
7-7
Polygons
The sum of the interior angle measures in a triangle is 180°, so the sum of the interior angle measures in a quadrilateral is 360°.

11. Understand the Problem
Course 1
7-7
Polygons
Additional Example 2: Problem Solving Application
Malcolm designed a wall hanging that was a regular 9-sided polygon (called a nonagon). What is the measure of each angle of the nonagon? 1
Understand the Problem
The answer will be the measure of each angle in a nonagon.
List the important information:
A regular nonagon has 9 congruent sides and 9 congruent angles.

12. Additional Example 2 Continued
Course 1
7-7
Polygons
Additional Example 2 Continued 2
Make a Plan
Make a table to look for a pattern using regular polygons.
Solve 3
Draw some regular polygons and divide each into triangles.

13. Additional Example 2 Continued
Course 1
7-7
Polygons
Additional Example 2 Continued
720°

14. Additional Example 2 Continued
Course 1
7-7
Polygons
Additional Example 2 Continued
The number of triangles is always 2 fewer than the number of sides.
A nonagon can be divided into 9 – 2 = 7 triangles.
The sum of the interior angle measures in a nonagon is 7  180° = 1,260°.
So the measure of each angle is 1,260° ÷ 9 = 140°.

15. Additional Example 2 Continued
Course 1
7-7
Polygons
Additional Example 2 Continued 4
Look Back
Each angle in a nonagon is obtuse. 140° is a reasonable answer, because an obtuse angle is between 90° and 180°.

16. Understand the Problem
Course 1
7-7
Polygons
Try This: Additional Example 2
Sara designed a picture that was a regular 6-sided polygon (called a hexagon). What is the measure of each angle of the hexagon? 1
Understand the Problem
The answer will be the measure of each angle in a hexagon.
List the important information:
A regular hexagon has 6 congruent sides and 6 congruent angles.

17. Try This: Example 2 Continued
Course 1
7-7
Polygons
Try This: Example 2 Continued 2
Make a Plan
Make a table to look for a pattern using regular polygons.
Solve 3
Draw some regular polygons and divide each into triangles.

18. Try This: Example 2 Continued
Course 1
7-7
Polygons
Try This: Example 2 Continued

19. Try This: Example 2 Continued
Course 1
7-7
Polygons
Try This: Example 2 Continued
The number of triangles is always 2 fewer than the number of sides A hexagon can be divided into 6 – 2 = 4 triangles.
The sum of the interior angles in a octagon is  180° = 720°.
So the measure of each angle is 720° ÷ 6 = 120°.

20. Try This: Example 2 Continued
Course 1
7-7
Polygons
Try This: Example 2 Continued 4
Look Back
Each angle in a hexagon is obtuse. 120° is a reasonable answer, because an obtuse angle is between 90° and 180°.

21. Insert Lesson Title Here
Course 1
7-7
Polygons
Insert Lesson Title Here
Lesson Quiz
1. Name each polygon and tell whether it appears to be regular or not regular.
2. What is the measure of each angle in a regular dodecagon (12-sided figure)?
nonagon, regular; octagon, not regular
150°