1. 5.1 Quadrilaterals

2. Quadrilateral:_________________________ Parallelogram:_______________________

3. More Parallelogram Characteristics Theorem 5.1:____________________________ Theorem 5.2:___________________________ Theorem 5.3:___________________________

4. Examples 6 9 b a 80 xy x y 45 35 9 2b 12 a

5. 3. Find the perimeter of parallelogram PINE if PI=12 and IN=8. PI N E 12 8 A B C GF D E

6. 2x+18 18 4y-22 22 X=_______ y=_______ 6. 7. 11x 45 80 4y+5 X=_______ y=_______ Which to solve 1 st ?

7. True or False: 1.Every parallelogram is a quadrilateral? 2.Every Quad is a parallelogram? 3.All angles of a parallelogram are congruent? 4.All sides of a parallelogram are congruent? 5.In RSTU, RS is parallel to TU? 6.In XWYZ, XY=WZ ? 7.In ABCD, if angle A=50, then C=130?

8. 5.2 Proving Parallelograms

9. Ways to Prove Quadrilaterals are Parallelograms Theorem 5.4: _____________________________ ________________________________________ Theorem 5.5: _____________________________ ________________________________________ Theorem 5.6: _____________________________ ________________________________________

10. Theorem 5.7:_____________________ ___________________________________ 5 ways to prove a quad is a Parallelogram 1. 2. 3. 4. 5.

11. A C B D E 1 2 5 6 8 7 4 3 910

12. A C B D E 1 2 5 6 8 7 4 3 9 F 11 12

13. A CF B D E 1 2 1056 879 4 3

14. 5.3 Parallel Lines

15. Theorems involving Parallel Lines Theorem 5.8:_______________________ _____________________________________

16. Theorem 5.9:____________________ __________________________________

17. Theorem 5.10:______________________ ____________________________________

18. Theorem 5.11:______________________ ____________________________________

19. C R ATB S R, S, T are Midpoints. ABBCACSTTRRS a) b) c) 121418 152210 596

20. R S T A B C 1.If RS=12 then ST=_______ 2.If AB=8 then BC=________ 3.If AC=20 then AB=_______ 4.If AC=10x then BC=______

21. C X AZB Y R, S, T are Midpoints. ABBCACXYXZZY a) b) K 2k+3 24 968

22. 5.4 Special Parallelograms

23. Special Parallelograms Rectangle:___________________________ Rhombus:___________________________ Square: _____________________________

24. Theorems for Special Parallelograms Theorem 5.12: ______________________ ___________________________________ Theorem 5.13:_______________________ ___________________________________ Theorem 5.14: _______________________ ___________________________________

25. Theorem 5.15:_____________________ ___________________________________

26. Proving a Rhombus or Rectangle Theorem 5.16:_______________________ _____________________________________ Theorem 5.17:_______________________ _____________________________________

27. PropertyParallelogram Rect.Rhombus Square

28. Examples: ABCD is a Rhombus AB C D 62 E

29. M N PO L MNOP is a Rectangle 29 12

30. 1 2 3 W Y Z X

31. A C B DE 12

32. 5.5 Trapezoids

33. Warmup: Always, Never or Sometimes 1.A square is________ a rhombus. 2.The diagonals of a parallelogram _________ bisect the angles of a parallelogram. 3.The diagonals of a rhombus are _________ congruent. 4.A rectangle _________ has consecutive sides congruent. 5.The diagonals of a parallelogram are _________ perpendicular bisectors of each other

34. Trapezoids Trapezoid:_______________________ _____________________________________ ________________________ Isosceles Trapezoid _____________________ ______________________________________

36. Trapezoid Theorems Theorem 5.18:______________________ __________________________________

37. Theorem 5.19:________________________ ______________________________________

38. AB C D XY ZW Solve: AB=10; DC=12 Find YW=_____ ZX=_____ XY=_____ 10 12

39. A B CD FE 1.If AB=25, DC=13 then EF=_______ 2.If AE=11, FB=8 then AD=______ BC=______ 3.If AB=29 and EF=24 then DC=_____ 4.If AB=7y+6, EF=5y-3, and DC=y-5 then y=__

40. 4 x y Find x=_______ y=_______

41. Quad TUNE is an isosiceles trapezoid with TU and NE as bases. If angle U equals 62 degrees find the measures of the other 3 angles.