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Angles of Polygons

Angles of Polygons. Let's Discuss. What does the word “polygon” mean?. What is the smallest number of sides a polygon can have?. What is the largest number of sides a polygon can have?. Triangle. Octagon. Quadrilateral. Nonagon. Pentagon. Decagon. Dodecagon. Hexagon. n-gon. Heptagon.

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Angles of Polygons

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  1. Angles of Polygons

  2. Let's Discuss What does the word “polygon” mean? What is the smallest number of sides a polygon can have? What is the largest number of sides a polygon can have?

  3. Triangle Octagon Quadrilateral Nonagon Pentagon Decagon Dodecagon Hexagon n-gon Heptagon Hendecagon

  4. Hip Bone’s connected to the…Classifying Polygons Polygons with 3 sides… Triangles Polygons with 4 sides… Quadrilaterals Polygons with 5 sides.. Pentagons But wait we have more polygons Polygons with 6 sides… Hexagons Polygons with 7 sides… Heptagons Polygons with 8 sides… Octagons But still we have more polygons Polygons with 9 sides… Nonagons Polygons with 10 sides… Decagons Polygons with 12 sides… Dodecagons And now we have our polygons

  5. A VERTEX is the point of intersection of two sides CONSECUTIVE VERTICESare two endpoints of any side. A B F C A segment whose endpoints are two nonconsecutive vertices is called a DIAGONAL. E D Sides that share a vertex are called CONSECUTIVE SIDES. Important Terms

  6. Polygons are named by listing its vertices consecutively. A B C F E D

  7. More Important Terms EQUILATERAL - All sides are congruent EQUIANGULAR - All angles are congruent REGULAR- All sides and angles are congruent

  8. Interior Angles Exterior Angles Three more important terms SUPPLEMENTARY the SUM of an interior angle and it’s corresponding exterior angle = 180o

  9. Polygons can be CONCAVE or CONVEX CONCAVE CONVEX

  10. Classify each polygon as convex or concave. Concave Concave Concave CONVEX

  11. It’s what’s inside that counts  Finding and using the interior angle measures of polygons

  12. What is the sum of the measures of the interior angles of a triangle? 180° 180° 180° What is the sum of the measures of the interior angles of any quadrilateral? 360°

  13. Sum of measures of interior angles # of triangles # of sides 1(180) = 180 3 1 2(180) = 360 4 2 3 3(180) = 540 5 6 4 4(180) = 720 n-2 (n-2) 180 n

  14. If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180°)

  15. If you know the sum of the angles of a regular polygon, how can you find the measure of one of the congruent angles?

  16. If a regular convex polygon has n sides, then the measure of one of the interior angles is

  17. HOMEWORK pg 300 1-15

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