1. 7-4 Classifying Polygons Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up 1. How many sides does a hexagon have? 2. How many sides does a pentagon have? 3. How many angles does an octagon have? 4. Evaluate (n – 2)180 for n = 7. Course 3 7-4 Classifying Polygons 6 5 8 900

3. Problem of the Day Jeffrey planted four carnations, three dahlias, seven marigolds, five cornflowers, one geranium, and four mums. He forgot to water them and on each of the two following days, half the remaining flowers died. How many flowers were still living at the end of the second day? 6 Course 3 7-4 Classifying Polygons

4. Learn to classify and find angles in polygons. Course 3 7-4 Classifying Polygons

5. Vocabulary polygon regular polygon trapezoid parallelogram rectangle rhombus square Insert Lesson Title Here Course 3 7-4 Classifying Polygons

6. A polygon is a closed plane figure formed by three or more segments. A polygon is named by the number of its sides. Course 3 7-4 Classifying Polygons

7. nn-gon 8Octagon 7Heptagon 6Hexagon 5Pentagon 4Quadrilateral 3Triangle Number of Sides Polygon Course 3 7-4 Classifying Polygons

8. Additional Example 1A: Finding Sums of the Angle Measures in Polygons Find the sum of the angle measures in a hexagon. 4 180° = 720° 4 triangles Divide the figure into triangles. Course 3 7-4 Classifying Polygons

9. Additional Example 1B: Finding Sums of the Angle Measures in Polygons Continued Find the sum of the angle measures in a octagon. 6 180° = 1080° 6 triangles Divide the figure into triangles. Course 3 7-4 Classifying Polygons

10. Check It Out: Example 1A Find the sum of the angle measures in a hexagon. 4 180° = 720° 4 triangles Divide the figure into triangles. Course 3 7-4 Classifying Polygons

11. Find the sum of the angle measures in a heptagon. 5 180° = 900° 5 triangles Check It Out: Example 1B Divide the figure into triangles. Course 3 7-4 Classifying Polygons

12. The pattern is that the number of triangles is always 2 less than the number of sides. So an n-gon can be divided into n – 2 triangles. The sum of the angle measures of any n-gon is 180°(n – 2). All the sides and angles of a regular polygon have equal measures. Course 3 7-4 Classifying Polygons

13. Additional Example 2A: Finding the Measure of Each Angle in a Regular Polygon Find the angle measures in the regular polygon. 6 congruent angles 6x° = 180°(6 – 2) 6x° = 180°(4) 6x° = 720° 6x° 66x° 6 720° 6 = x° = 120° Course 3 7-4 Classifying Polygons

14. Additional Example 2B: Finding the Measure of Each Angle in a Regular Polygon Find the angle measures in the regular polygon. 4 congruent angles 4y° = 180°(4 – 2) 4y° = 180°(2) 4y° = 360° y° = 90° 4y° 44y° 4 360° 4 = Course 3 7-4 Classifying Polygons

15. Check It Out: Example 2A Find the angle measures in the regular polygon. 5 congruent angles 5a° = 180°(5 – 2) 5a° = 180°(3) 5a° = 540° 5a°55a°5 540° 5 = a° = 108° a° Course 3 7-4 Classifying Polygons

16. Find the angle measures in the regular polygon. 8 congruent angles 8b° = 180°(8 – 2) 8b° = 180°(6) 8b° = 1080° 8b° 88b° 8 1080° 8 = b° = 135° b° Check It Out: Example 2B Course 3 7-4 Classifying Polygons

17. Quadrilaterals with certain properties are given additional names. A trapezoid has exactly 1 pair of parallel sides. A parallelogram has 2 pairs of parallel sides. A rectangle has 4 right angles. A rhombus has 4 congruent sides. A square has 4 congruent sides and 4 right angles. Course 3 7-4 Classifying Polygons

18. Course 3 7-4 Classifying Polygons

19. Additional Example 3A: Classifying Quadrilaterals quadrilateral parallelogram rectangle rhombus square Four-sided polygon 2 pairs of parallel sides 4 right angles 4 congruent sides 4 congruent sides and 4 right angles Give all the names that apply to the figure. Course 3 7-4 Classifying Polygons

20. Additional Example 3B: Classifying Quadrilaterals Give all the names that apply to the figure. quadrilateral parallelogram rhombus Four-sided polygon 2 pairs of parallel sides 4 congruent sides Course 3 7-4 Classifying Polygons

21. Check It Out: Example 3A Give all the names that apply to the figure. quadrilateral parallelogram rectangle Four-sided polygon 2 pairs of parallel sides 4 right angles Course 3 7-4 Classifying Polygons

22. Give all the names that apply to the figure. quadrilateral Four-sided polygon Check It Out: Example 3B Course 3 7-4 Classifying Polygons

23. Lesson Quiz: Part I 1. Find the sum of the angle measures in a quadrilateral. 2. Find the sum of the angle measures in a hexagon. 3. Find the measure of each angle in a regular octagon. Insert Lesson Title Here 360° 720° 135° Course 3 7-4 Classifying Polygons

24. Lesson Quiz: Part II 4. Write all of the names that apply to the figure below. Insert Lesson Title Here quadrilateral, rhombus, parallelogram Course 3 7-4 Classifying Polygons