The Quadrilateral Family Tree

1. The Quadrilateral Family Tree Wednesday 12/3/08 – Thursday 12/4/08

2. ________________________ 1. _____________________ __________ _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. _____________________ 2. _____________________ 3. _______________ 3. _____________________ 4. _____________________ __________________ _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. _____________________ 2. _____________________ 3. _____________________ 2. _____________________ 3. _____________________ 3. _____________________ 4. _____________________ _____________________ 1. _____________________ 2. _____________________

3. Quadrilateral __________ _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. _____________________ 2. _____________________ 3. _______________ 3. _____________________ 4. _____________________ __________________ _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. _____________________ 2. _____________________ 3. _____________________ 2. _____________________ 3. _____________________ 3. _____________________ 4. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. Four-sided polygon

4. Parallelograms

5. Parallelogram • A quadrilateral with two pairs of parallel sides

6. QUADRILATERAL 1. Four-sided polygon Kite Trapezoid 1. Parallelogram 1. 1. 2. 2. 3. 3. 4. Isosceles Trapezoid 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2.

7. Parallelogram

8. Parallelogram

9. Parallelogram 2 1

10. Parallelogram 2 1

11. Parallelogram 3 2 1 4

12. Parallelogram 3 2 1 4

13. Parallelogram 3 2 1 4

14. Parallelogram 3 2 1 4

15. Parallelogram • The two triangles formed by a diagonal are congruent by ASA. 3 2 1 4

16. Parallelogram • What does that mean about opposite sides of a parallelogram? 3 2 1 4

17. Parallelogram • What does that mean about opposite sides of a parallelogram? 3 2 1 4

18. Quadrilateral 1. Four-sided polygon Kite TRAPEZOID 1. PARALLELOGRAM 1. 1. 2. 2. 3. 3. 4. Isosceles Trapezoid Rhombus 1. Rectangle 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2.

19. QUADRILATERAL 1. Four-sided polygon Parallelogram 1. 2. 3. 4. 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

20. Parallelograms • What about opposite angles in a parallelogram?

21. QUADRILATERAL 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. 4. 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

22. Parallelograms • Are these two triangles congruent? By which postulate? 2 1

23. Parallelogram • Since the triangles are congruent, the diagonals of the parallelogram bisect each other.

24. QUADRILATERAL 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. Diagonals bisect each other 4. 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

25. Parallelogram • What kind of angles are angles 5 & 6? 5 6

26. Parallelogram • Consecutive angles in a parallelogram are supplementary. 5 6

27. QUADRILATERAL 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. Diagonals bisect each other 4. Consecutive angles are supp. 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

28. Special Parallelograms Rectangles, rhombuses, and squares

29. Rectangles

30. Rectangle • A quadrilateral with four right angles

31. Rectangle • Has all the properties of a parallelogram

32. Quadrilateral 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. Diagonals bisect each other 4. Consecutive angles are supp. RECTANGLE 1. 1. 1. Four right angles 2. 2. 3. 2. All properties above 3. 4. 3. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

33. Rectangle • What should be true about the overlapping triangles formed by the diagonals?

34. Rectangle • What should be true about the overlapping triangles formed by the diagonals?

35. Rectangle • The triangles are congruent by SAS since opposite sides of a parallelogram are congruent

36. Rectangle • So the diagonals in a rectangle must be congruent by CPCTC

37. Quadrilateral 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. Diagonals bisect each other 4. Consecutive angles are supp. RECTANGLE 1. 1. 1. Four right angles 2. 2. 3. 2. All properties above 3. 4. 3. Diagonals are congruent Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

38. Rhombuses

39. Rhombus • A quadrilateral with four congruent sides

40. Rhombus • Also has all the properties of a parallelogram

41. Quadrilateral 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. Diagonals bisect each other 4. Consecutive angles are supp. RHOMBUS RECTANGLE 1. 1. Four congruent sides 1. Four right angles 2. All properties above 2. 3. 2. All properties above 3. 4. 3. Diagonals are congruent Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

42. Rhombus • What kind of triangles are formed by a diagonal?

43. Rhombus • What kind of triangles are formed by a diagonal?

44. Rhombus • What kind of triangles are formed by a diagonal?

45. Rhombus • Each diagonal bisects a pair of opposite angles

46. Rhombus • Each diagonal bisects a pair of opposite angles

47. Quadrilateral 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. Diagonals bisect each other 4. Consecutive angles are supp. RHOMBUS 1. Four congruent sides RECTANGLE 1. 2. All properties above 1. Four right angles 2. 3. Diagonals bisect opposite angles 2. All properties above 3. 3. Diagonals are congruent 4. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

48. Rhombus

49. Rhombus • What should be true about angles 1 and 2? 2 1

50. Rhombus • What would the angle measures have to be? 2 1