1. 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

2. 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

3. Learn to classify and find angles in polygons. Course 3 7-4 Classifying Polygons TB P. 341-345

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

5. 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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. Course 3 7-4 Classifying Polygons

14. 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

15. 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

16. 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

17. 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