2. * Quadrilateral I have exactly four sides.

3. *Trapezoid I have only one set of parallel sides. [The median of a trapezoid is parallel to the bases and equal to one-half the sum of the bases.]

5. Isosceles Trapezoid I have: - only one set of parallel sides - base angles congruent - legs congruent - diagonals congruent - opposite angles supplementary

6. Parallelogram I have: - 2 sets of parallel sides - 2 sets of congruent sides - opposite angles congruent - consecutive angles supplementary - diagonals bisect each other - diagonals form 2 congruent triangles

8. TRAPEZOIDS -quadrilateral with one pair of parallel sides

9. TRAPEZOIDS -parallel sides bases

10. TRAPEZOIDS -pair of angles that share a base base angles

11. TRAPEZOIDS -pair of angles that share a base base angles

12. Open books to page 291. Work on investigation 6.3.2 on your own.

13. Trapezoid Consecutive Angles Conjecture The consecutive angles between the bases of a trapezoid are ______________. supplementary

14. TRAPEZOIDS m  1 + m  2 =180° m  3 + m  4 =180°

15. TRAPEZOIDS -two nonparallel sides are congruent isosceles trapezoid

16. Isosceles Trapezoid Conjecture The base angles of an isosceles trapezoid are ______________. congruent

17. TRAPEZOIDS m  1 = m  4 m  2 = m  3

18. Isosceles Trapezoid Diagonals Conjecture The diagonals of an isosceles trapezoid are ______________. congruent

19. TRAPEZOIDS mAC = mBD

20. Properties of Parallelograms Objectives: 1. Discover properties of parallelograms.

21. parallelogram: -quadrilateral whose opposite sides are parallel

23. Parallelogram I have: - 2 sets of parallel sides - 2 sets of congruent sides - opposite angles congruent - consecutive angles supplementary - diagonals bisect each other - diagonals form 2 congruent triangles

25. parallelogram: -quadrilateral whose opposite sides are parallel

26. 1. In your notes, use a ruler to create a parallelogram.

27. 2. With your protractor, measure each interior angle of your parallelogram. 1 1 2 °

28. 3. What can you say about opposite angles of a parallelogram? Compare your parallelogram other parallelograms around you. 1 1 2 °

29. The _______________of a parallelogram are ________. opposite angles congruent

30. What is the measure of  A? 127°

31. What is the measure of  B? 53°

32. consecutive angles - angles that share a side 112°

33. consecutive angles - one set of consecutive angles 112°

34. A relationship exists between consecutive angles of a parallelogram. 4. Find the sum of the measures of each pair of consecutive angles in your parallelogram.

35. The _______________of a parallelogram are _____________. consecutive angles supplimentary

36. What is the measure of  C? 38°

37. What is the measure of  D? 86°

38. What is the measure of  E? 94°

39. What is the measure of  F? 86°

40. 5. Use your compass to compare the measures of opposite sides of a parallelogram.

41. The _______________of a parallelogram are _____________. opposite sides congruent

42. The perimeter of parallelogram ABCD is 48m.

43. perimeter = 48m mAD=?

44. perimeter = 48m mAD = 16m

45. perimeter = 48m mAB=?

46. perimeter = 48m mAB= 8m

47. perimeter = 48m mCD= ?

48. perimeter = 48m mCD= 8m

49. 6.Construct the two diagonals on your parallelogram. The diagonals intersect each other.

50. Do the diagonals bisect each other? YES Use your compass to check.

51. The _______________of a parallelogram _________________. diagonals bisect each other

52. mIN=5 inches mNH =?

53. mIN=5 inches mNH = 5 inches

54. Properties of Special Parallelograms Objectives 1. Discover special properties of a rectangle, rhombus, and square.

56. rhombus -quadrilateral with four congruent sides

57. If two parallel lines are intersected by a second pair of parallel lines the same distance apart as the first pair, then the parallelogram formed is a ___________. rhombus

58. The diagonals of a rhombus are perpendicular bisectors of each other.

59. states that the diagonals intersect at right angles.

60. The diagonals of a rhombus bisect the angles of the rhombus.

61. states that the diagonals bisect each angle of the rhombus so…..

64. rectangle - equiangular parallelogram

65. The measure of each angle of a rectangle is ___°. 90

66. rectangle Each angle of a rectangle has the measure of 90°

67. The diagonals of a rectangle are ____________. equal length

68. equal length

69. The diagonals of a rectangle are ____________. equal length

71. square -equiangular rhombus -equilateral rectangle