1 / 20

Chapter 5

Chapter 5. HOMEWORK: Lesson 5.1/1-14. 5.1 The Polygon Angle-Sum Theorem. Objectives. Define polygon, concave / convex polygon, and regular polygon Find the sum of the measures of interior angles of a polygon. Definition of polygon.

harvey
Download Presentation

Chapter 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 5 HOMEWORK: Lesson 5.1/1-14 5.1 The Polygon Angle-Sum Theorem

  2. Objectives • Define polygon, concave / convex polygon, and regular polygon • Find the sum of the measures of interior angles of a polygon

  3. Definition of polygon • A polygon is a closed plane figure formed by 3 or more sides that are line segments; • the segments only intersect at endpoints • no adjacent sides are collinear • Polygons are named using letters of consecutive vertices

  4. Concave and Convex Polygons • A convex polygon has no diagonal with points outside the polygon • A concave polygon has at least one diagonal with points outside the polygon

  5. Regular Polygon Definition • An equilateral polygon has all sides congruent • An equiangular polygon has all angles congruent • A regular polygon is both equilateral and equiangular Note:A regular polygon is always convex

  6. Polygon Angle-Sum Theorem The sum of the measures of the angles of an n-gon is SUM = (n-2)180 ex: A pentagon has 5 sides.

  7. Sum of Interior Angles in Polygons

  8. Sum of Interior Angles Find m∠ X The sum of the measures of the interior angles for a quadrilateral is (4 – 2) * 180 = 360 The marks in the illustration indicate that m∠X = m∠Y = x So the sum of all four interior angles is x + x + 100 + 90 = 360 2 x + 190 = 360 2 x = 170 m∠X = 85

  9. Polygon NamesMEMORIZE THESE! 3 sides Triangle 4 sides Quadrilateral 5 sides Pentagon 6 sides Hexagon 7 sides Heptagon 8 sides Octagon 9 sides Nonagon 10 sides Decagon 11 sides Undecagon 12 sides Dodecagon n sides n-gon

  10. Naming A Polygon A polygon is named by the number of_____. ex: If a polygon has ___ sides, you use ___ letters. Polygon ABCDE SIDES 5 5

  11. Example #1 ABCDEF CDEFAB 1. Name________. Is it concave or convex?__________ 2. Name ________ Is it concave or convex?__________ concave DEABC ABCDE convex 1 2

  12. Example #2 • Find the interior angle sum. a. 13-gon b. decagon (n – 2) 180 (13 – 2) 180 (11) 180 1980˚ (n – 2) 180 (10 – 2) 180 (8) 180 1440˚

  13. The Number of Sides Use polygon SUM formula to find the number of sides in a REGULAR or EQUIANGULAR polygon SUM = (n– 2) 180 Given (or calculate) the sum of the angles Solve for n

  14. Example #3 How many sides does each regular polygon have if its interior angle sum is: a. 2700 b. 1080 Sum is given 1080 = (n – 2) 180 1080 = (n – 2) 180 6 = n – 2 8 = n Octagon 2700 = (n – 2) 180 2700 = (n – 2) 180 15 = n – 2 17 = n 17-gon

  15. ONE angle in a Polygon Use polygon SUM and the number of sides in a REGULAR or EQUIANGULAR polygon to find ONE angle ONE = (n – 2) 180 = SUM n n Given (or calculate) the sum of the angles Solve for ONE

  16. Example #5 Find y First calculate pentagon sum Pentagon sum = 540˚ Sum is calculated 540 = 5 y 540 = y 5 108˚ = y

  17. Example #6 Find x. Hexagon sum = 720˚ one angle of an equiangular hexagon SUM = 720 = 120˚ 6 6 120˚ x makes a linear pair with an interior angle x = 60˚ x = 180˚ – 120˚ = 60˚

  18. Summary: SUM of the Interior Angles of a Polygon S = (n – 2) 180 One Interior Angle of a REGULAR Polygon One = (n – 2) 180 = SUM n n

  19. Example #7 Find x. Heptagon sum = 900° 900 = x + 816 132 100 155 142 167 +120 816 84 = x

More Related