1. Tuesday, March 4 Chapter13-4 Two Dimensional Figures

2. Objective: To understand sides and angles of polygons.

3. Two Dimensional Figures A polygon is a simple closed, two dimensional figure with three or more sides. The number of sides will determine a polygon’s name.

4. Two Dimensional Figures When all of the sides and angles of a polygon are congruent, the polygon is a regular polygon. If the sides are not congruent, the polygon is irregular.

5. Two Dimensional Figures A triangle has three sides and three angles. The inside angles of a triangle will always add to 180 °.

6. Two Dimensional Figures Certain triangles have specific names: A scalene triangle has no congruent sides.

7. Two Dimensional Figures Certain triangles have specific names: An isosceles triangle has two sides congruent.

8. Two Dimensional Figures Certain triangles have specific names: An equilateral triangle has all sides congruent.

9. Two Dimensional Figures A quadrilateral has four sides. The inside angles of a quadrilateral will always add to 360 °.

10. Two Dimensional Figures Certain quadrilaterals have specific names: A rectangle has opposite sides that are congruent and parallel, and all angles are right angles.

11. Two Dimensional Figures Certain quadrilaterals have specific names: A square has all sides that are congruent and parallel, and all angles are right angles.

12. Two Dimensional Figures Certain quadrilaterals have specific names: A parallelogram has opposite sides that are congruent and parallel, and opposite angles are congruent.

13. Two Dimensional Figures Certain quadrilaterals have specific names: A rhombus has all sides that are congruent, opposite sides are parallel and opposite angles are congruent.

14. Two Dimensional Figures A pentagon has five sides. The inside angles of a pentagon will always add to 540 °.

15. Two Dimensional Figures A hexagon has six sides. The inside angles of a hexagon will always add to 720 °.

16. Two Dimensional Figures A heptagon has seven sides. The inside angles of a heptagon will always add to 900 °.

17. Two Dimensional Figures A octagon has eight sides. The inside angles of a octagon will always add to 1080 °.

18. Two Dimensional Figures A nonagon has nine sides. The inside angles of a nonagon will always add to 1260 °.

19. Two Dimensional Figures A decagon has ten sides. The inside angles of a decagon will always add to 1440 °.

20. Two Dimensional Figures The formula to find the sum of the inside angles of any polygon is the number of sides minus 2 then multiply by 180, or (n-2)180.

21. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

22. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular quadrilateral (parallelogram) Since the polygon has 4 sides it is a quadrilateral. Since all sides are not congruent, it is irregular.

23. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular quadrilateral (parallelogram) Three of the inside angles add to 333˚. What is the remaining angle?

24. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular quadrilateral (parallelogram) Three of the inside angles add to 333˚. What is the remaining angle? 360˚ – 333˚ = 27˚

25. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

26. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. irregular hexagon Since the polygon has 6 sides it is a hexagon. Since all sides are not congruent, it is irregular.

27. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. irregular hexagon Five of the inside angles add to 685˚. What is the remaining angle?

28. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. irregular hexagon Five of the inside angles add to 685˚. What is the remaining angle? 720˚ – 685˚ = 35˚

29. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

30. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Regular quadrilateral (square) Since the polygon has 4 sides it is a quadrilateral. Since all sides are congruent, it is regular.

31. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

32. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (isosceles) How do we know two sides are congruent?

33. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (isosceles) Since the opposite angles are the same, the sides are the same length.

34. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

35. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular pentagon Since the polygon has 5 sides it is a pentagon. Since all sides are not congruent, it is irregular.

36. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular pentagon Four of the inside angles add to 497˚. What is the remaining angle?

37. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular pentagon Four of the inside angles add to 497˚. What is the remaining angle? 540˚ – 497˚ = 43˚

38. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

39. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (scalene) Since the polygon has 3 sides it is a triangle. Since all sides are not congruent, it is irregular (scalene).

40. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (scalene) Two of the inside angles add to 129˚. What is the remaining angle?

41. Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (scalene) Two of the inside angles add to 129˚. What is the remaining angle? 180˚ – 129˚ = 51˚

42. Two Dimensional Figures What do you say when you see an empty parrot cage?

43. Two Dimensional Figures What do you say when you see an empty parrot cage? polygon

44. Two Dimensional Figures Agenda Notes – Homework – Practice Skills 13-4 Due Wednesday, March 5 Chapter 13 Test Monday, March 10