1 / 16

The Polygon Angle-Sum Theorems

The Polygon Angle-Sum Theorems. 3.4 The Polygon Angle-Sum Theorems. Polygon: a closed plane figure with at least three sides that are segments. Not a polygon; Not enclosed. Not a polygon; Two sides intersect. A polygon. Naming a Polygon. Name a polygon by its vertices. A.

Download Presentation

The Polygon Angle-Sum Theorems

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. The Polygon Angle-Sum Theorems

  2. 3.4 The Polygon Angle-Sum Theorems Polygon: a closed plane figure with at least three sides that are segments Not a polygon; Not enclosed Not a polygon; Two sides intersect A polygon

  3. Naming a Polygon Name a polygon by its vertices. A ABCDE or AEDCB Start at one vertex and go around in order B E C D

  4. Naming a Polygon Three polygons are pictured. Name each polygon: L P M O N

  5. Classifying a Polygon by the number of sides:

  6. Convex vs. Concave • A Convex Polygon has all vertices pointing “out” • A Concave Polygon has one or more vertices “caving in”

  7. Classify • Classify each polygon by its sides. Identify each as convex or concave:

  8. Sum of Polygon Angle Measures Use triangles to figure out the sum of the angles in each polygon: # of Sides: # of Triangles: Total Degrees: # of Sides: # of Triangles: Total Degrees:

  9. Sum of Polygon Angle Measures

  10. Theorem 3-9 Polygon Angle Sum Theorem The sum of the measures of the angles in a polygon is (n – 2)180. Find the sum of the measure of the angles of a 15-gon.

  11. Polygon Angle Sum The sum of the measures of the angles of a given polygon is 720. How many sides does the polygon have? Use (n – 2)180 :

  12. Using Polygon Angle-Sum Theorem Find the measure of <Y in pentagon TVYMR at the right. R T Use (n – 2)180 135° M 90° Y V Write an equation to solve for <Y

  13. Using Polygon Angle-Sum Theorem Pentagon ABCDE has 5 congruent angles. Find the measure of each angle. Use the Polygon Angle-Sum Theorem: (n – 2)180 Divide the total number of degrees by the number of angles:

  14. Exterior Angles What do you notice about each set of exterior angles? 80° 75° 115° 2 1 150° 99° 130° 71° 70° 88° 1: 86° 3 2: 3: 70° 46°

  15. Theorem 3-10 Polygon Angle-Sum Theorem The sum of one set of exterior angles for any polygon is 360°. 1 5 2 4 3 m<1 + m<2 + m<3 + m<4 + m<5 = 360°

  16. Polygons • Equilateral Polygon: all sides congruent • Equiangular Polygon: all angles congruent • Regular Polygon: all sides and all angles congruent (equiangular and equilateral) *If a polygon is a regular polygon then all of the exterior angles are also congruent.

More Related