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5-4. Polygons. Warm Up. Problem of the Day. Lesson Presentation. Pre-Algebra. 5-4. Polygons. Pre-Algebra. 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.

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5-4

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  1. 5-4 Polygons Warm Up Problem of the Day Lesson Presentation Pre-Algebra

  2. 5-4 Polygons Pre-Algebra 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. 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. Learn to classify and find angles in polygons.

  5. Vocabulary polygon regular polygon trapezoid parallelogram rectangle rhombus square

  6. The cross section of a brilliant-cut diamond is a pentagon. The most beautiful and valuable diamonds have precisely cut angles that maximize the amount of light they reflect. A polygon is a closed plane figure formed by three or more segments. A polygon is named by the number of its sides.

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

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

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

  10. Try This: Example 1A A. Find the sum of the angle measures in a hexagon. Divide the figure into triangles. 4 triangles 4 • 180° = 720°

  11. Try This: Example 1B B. Find the sum of the angle measures in a heptagon. Divide the figure into triangles. 5 triangles 5 • 180° = 900°

  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.

  13. 6x 6 720°6 = 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. 4y 4 360°4 = 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. 5a 5 540° 5 = Try This: 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. b° b° b° b° b° b° 8b 8 1080° 8 = b° b° Try This: 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. 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

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

  19. Try This: Example 3A Give all the names that apply to the figure. A. quadrilateral Four-sided polygon parallelogram 2 pairs of parallel sides rectangle 4 right angles

  20. Try This: Example 3B Give all the names that apply to the figure. B. quadrilateral Four-sided polygon

  21. Lesson Quiz: Part 1 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°

  22. Lesson Quiz: Part 2 4. Write all of the names that apply to the figure below. quadrilateral, rhombus, parallelogram

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