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7-4

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

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7-4

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

  2. 7-4 Classifying Polygons Course 3 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. 6 5 8 900

  3. 7-4 Classifying Polygons Course 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

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

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

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

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

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

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

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

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

  12. 7-4 Classifying Polygons Course 3 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.

  13. 7-4 Classifying Polygons 6x° 6 720°6 = Course 3 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° x° = 120°

  14. 7-4 Classifying Polygons 4y° 4 360°4 = Course 3 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°

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

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

  17. 7-4 Classifying Polygons Course 3 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.

  18. 7-4 Classifying Polygons Course 3

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

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

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

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

  23. 7-4 Classifying Polygons Course 3 Insert Lesson Title Here 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. 360° 720° 135°

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

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