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Exploring Polygons: Shapes and Properties

Discover the fascinating world of polygons, from triangles to dodecagons. Learn about vertices, diagonals, interior angles, and classifications like concave and convex. Practice and master polygon concepts with helpful exercises. Let's delve into the realm of geometric shapes!

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Exploring Polygons: Shapes and Properties

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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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