1 / 41

5.1 Quadrilaterals

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

bazyli
Download Presentation

5.1 Quadrilaterals

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 5.1 Quadrilaterals

  2. Quadrilateral:_________________________ Parallelogram: _______________________

  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.

More Related