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5.1 Quadrilaterals. Quadrilateral :_________________________ Parallelogram : _______________________. More Parallelogram Characteristics. Theorem 5.1:____________________________ Theorem 5.2:___________________________ Theorem 5.3:___________________________. Examples. 6. y. x. 9. b.

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

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

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

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

7. True or False: • Every parallelogram is a quadrilateral? • Every Quad is a parallelogram? • All angles of a parallelogram are congruent? • All sides of a parallelogram are congruent? • In RSTU, RS is parallel to TU? • In XWYZ, XY=WZ ? • 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 B 1 7 2 8 9 10 E 6 3 4 5 D C

12. A 7 2 B 1 8 F 12 10 11 9 E 6 4 3 5 D C

13. A E B 2 8 7 9 1 3 10 5 6 4 D F C

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, S, T are Midpoints. R S A T B AB BC AC ST TR RS a) b) c) 12 14 18 15 22 10 5 9 6

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

21. C R, S, T are Midpoints. X Y A Z B AB BC AC XY XZ ZY a) b) K 24 2k+3 9 8 6

22. 5.4SpecialParallelograms

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. Property Parallelogram Rect. Rhombus Square

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

29. M N 29 MNOP is a Rectangle 12 L P O

30. Y 2 W 3 1 Z X

31. A B 2 1 D E C

32. 5.5 Trapezoids

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

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

35. Trapezoid Theorems Theorem 5.18:______________________ __________________________________

36. Theorem 5.19: ________________________ ______________________________________ ______________________________________ ______________________________________

37. Solve: AB=10; DC=12 Find YW=_____ ZX=_____ XY=_____ 10 A B Z W X Y C D 12

38. If AB=25, DC=13 then EF=_______ • If AE=11, FB=8 then AD=______ BC=______ • If AB=29 and EF=24 then DC=_____ • If AB=7y+6, EF=5y-3, and DC=y-5 then y=__ C D F E A B

39. Find x=_______ y=_______ 4 x y

40. 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.

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