1. Course 1 8-7 Polygons 8-7 Polygons Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. Course 1 8-7 Polygons Warm Up True or false? 1. Some trapezoids are parallelograms. 2. Some figures with 4 right angles are squares. 3. Some quadrilaterals have only one right angle. false true

3. Course 1 8-7 Polygons Problem of the Day Four square tables pushed together can seat either 8 or 10 people. How many people could 12 square tables pushed together seat? 14, 16, or 26 people

4. Course 1 8-7 Polygons Learn to identify regular and not regular polygons and to find the angle measures of regular polygons.

5. Course 1 8-7 Polygons Vocabulary polygon regular polygon

6. Course 1 8-7 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.

7. Course 1 8-7 Polygons An equilateral triangle has three congruent sides. Remember!

8. Course 1 8-7 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. The shape is a closed plane figure formed by 3 or more line segments. polygon There are 5 sides and 5 angles. pentagon All 5 sides do not appear to be congruent. not regular

9. Course 1 8-7 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. There are 8 sides and 8 angles. octagon The sides and angles appear to be congruent. regular The shape is a closed plane figure formed by 3 or more line segments. polygon

10. Course 1 8-7 Polygons Check It Out: 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. There are 4 sides and 4 angles. quadrilateral The sides and angles appear to be congruent. regular

11. Course 1 8-7 Polygons Check It Out: 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. There are 4 sides and 4 angles. quadrilateral All 4 sides do not appear to be congruent. not regular

12. Course 1 8-7 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°.

13. Course 1 8-7 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 t 9 congruent angles.

14. Course 1 8-7 Polygons 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. Additional Example 2 Continued

15. Course 1 8-7 Polygons 720° The prefixes in the names of the polygons tell you how many sides and angles there are. tri- = threequad- = four penta- = fivehexa- = six octa- = eight Reading Math Additional Example 2 Continued

16. Course 1 8-7 Polygons 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°. Solve Cont. 3 Additional Example 2 Continued

17. Course 1 8-7 Polygons Look Back 4 Each angle in a nonagon is obtuse. 140° is a reasonable answer, because an obtuse angle is between 90° and 180°. Additional Example 2 Continued

18. Course 1 8-7 Polygons Check It Out: 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.

19. Course 1 8-7 Polygons 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. Check It Out: Example 2 Continued

20. Course 1 8-7 Polygons 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 4  180° = 720°. So the measure of each angle is 720° ÷ 6 = 120°. Check It Out: Example 2 Continued Solve Cont. 3

21. Course 1 8-7 Polygons Look Back 4 Each angle in a hexagon is obtuse. 120° is a reasonable answer, because an obtuse angle is between 90° and 180°. Check It Out: Example 2 Continued

22. Course 1 8-7 Polygons 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)? 150° nonagon, regular; octagon, not regular