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NAMING POLYGONS

NAMING 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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NAMING POLYGONS

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  1. NAMING 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

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

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

  8. Polygons can be CONCAVE or CONVEX CONCAVE CONVEX

  9. Ex. 3 Classify each polygon as convex or concave. Concave Concave Concave CONVEX

  10. Diagonals & Angle Measures

  11. REVIEW: 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°

  12. 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

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

  14. Ex. 1 Use the regular pentagon to answer the questions. • Find the sum of the measures of the interior angles. • Find the measure of ONE interior angle 540° 108°

  15. Interior Angles Exterior Angles Two more important terms

  16. 2 1 3 5 4 If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°.

  17. If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 3 2

  18. If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 2 4 3

  19. Ex. 2 Find the measure of ONE exterior angle of a regular hexagon. 60°

  20. Ex. 3 Find the measure of ONE exterior angle of a regular heptagon. 51.4°

  21. Ex. 4 Each exterior angle of a polygon is 18. How many sides does it have? n = 20

  22. Ex. 5 The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle? 185°

  23. Ex. 6 The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle. 30°, 90°, 150°, and 90°

  24. Ex. 7 If each interior angle of a regular polygon is 150, then how many sides does the polygon have? n = 12

  25. Practice Time Practice Worksheet 10-2

  26. Homework: Page 406 # 16-32 even Page 411 # 8-18 all

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