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Pre-Algebra

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

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Pre-Algebra

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

  2. 5-4 Polygons Pre-Algebra 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.

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

  4. 5-4 Polygons Pre-Algebra 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°

  5. 5-4 Polygons Pre-Algebra 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°

  6. 5-4 Polygons Pre-Algebra 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.

  7. 6x 6 720°6 5-4 Polygons = Pre-Algebra 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°

  8. 4y 4 360°4 5-4 Polygons = Pre-Algebra 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°

  9. 5-4 Polygons Pre-Algebra

  10. 5-4 Polygons Pre-Algebra 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

  11. 5-4 Polygons Pre-Algebra 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

  12. 5-4 Polygons Pre-Algebra A polygon is a closed plane figure formed by three or more segments. A polygon is named by the number of its sides. All the sides and angles of a regular polygon have equal measures.

  13. 5-4 Polygons Pre-Algebra 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°

  14. 5-4 Polygons Pre-Algebra The pattern is that the number of triangles is always 2 less than the number of sides. The sum of the angle measures of any polygon is 180°(n – 2).

  15. 5-4 Polygons Pre-Algebra 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°

  16. 5a 5 540° 5 5-4 Polygons = Pre-Algebra 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°

  17. 8b 8 b° b° 1080° 8 5-4 Polygons = b° b° b° b° b° b° Pre-Algebra 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°

  18. 5-4 Polygons Pre-Algebra

  19. 5-4 Polygons Pre-Algebra 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. 5-4 Polygons Pre-Algebra Try This: Example 3B Give all the names that apply to the figure. B. quadrilateral Four-sided polygon

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