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Geometry WorksheetQuadrilateralsDo Now:Section:Name:9. The notation of parallelogram: .Write the definition of quadrilaterals:AB.DParts & Properties of the QuadrilateralsCQPName the parallelogram and show its parallel sides:SR.1. :Vertices that are endpoints of the same side.Theorems of ParallelogramExample: .10. Theorem of Dividing DiagonalsA diagonal divides a parallelogram into two congruenttriangles2. :Sides that have a common endpoint.Given: ABCD is a parallelogramProve: ABD CDBProof:Example: .3. :Sides that do not have a common endpoint.Example: .4. :Angles whose vertices are consecutive.Example: .5. :Angles whose vertices are not consecutive.Example: .6. :A line segment whose endpoints are two nonadjacentvertices of the quadrilateral.11. Theorem of Opposite SidesOpposite sides of a parallelogram are congruentGiven: ABCD is a parallelogramProve: BC DAProof:Example: .7. The sum of the measures of the angles of a quadrilateralis: . .Example: .Parallelograms8. Write the definition of parallelogram:.Mr. Lin1
Geometry WorksheetQuadrilateralsName:Ax 7ASection:15. ABCD is a parallelogram, ABCD is a parallelogram, ifAO 3, BO 4 AB 6, AC BD ?6DoNow:ABCD is a parallelogram, what’s the perimeter of ABCD ?By 234O2y – 6DDBCC3x - 316. ABCD is a parallelogram, if AO x 4, BO 2y-6, CO 3x-4, an DO y 2, solve for x and y.A12. Theorem of Opposite AnglesOpposite angles of a parallelogram are congruentB2y–6x 4 A C, and B Dy 2DGiven: ABCD is a parallelogramProve: A C, and B DProof:O3x–4C17. Theorem of Consecutive AnglesThe consecutive angles of asupplementaryparallelogramareGiven: ABCD is a parallelogramProve: A and B are supplementary C and D are supplementary A and D are supplementary B and C are supplementaryProof:13. ABCD is a parallelogram, what are the values of x andy?ABoox 20D180 o – yy – 202x–60 oC14. Theorem of Bisecting DiagonalsThe diagonals of a parallelogram bisect each otherGiven: ABCD is a parallelogramProve: AC and BD bisect each other at OProof: 18. ABCD is a parallelogram, what are the values of x, yAand z?oo120DMr. LinzoxyoC2B
Geometry WorksheetQuadrilaterals19. ABCD is a parallelogram, what are the values of x andy?ABoox 30x–30Name:23. Given: ABCD is a parallelogram, BO ODProve: EO OFEA y 20oDSection: C BODCF20. ABCD is a parallelogram, calculate the perimeter ofx 30ABCD?AB2y – 10y 10DC2x – 1024. Given: ABCD is a parallelogram, AF CEProve: FAB ECDABE F21. ABCD is a parallelogram, solve for x.ADx 30CBx–10Ox 102xD22. Given: ABCD is a parallelogramProve: XO YO CXABReview: Theorems of ParallelogramO DCYMr. Lin3
Geometry WorksheetQuadrilateralsProve Quadrilaterals are Parallelograms25. List the (A)Section:Name:29. Congruent Opposite SidesIf both pairs of opposite sides of a quadrilateral areparallel, then the quadrilateral is a parallelogramGiven: If AB CD , and BC DAProve: ABCD is a parallelogramProof: (B)(C)(D)(E)(F)26. Parallel Opposite SidesIf both pairs of opposite sides of a quadrilateral areparallel, then the quadrilateral is a parallelogramGiven: If AB CD , and BC DAProve: ABCD is a parallelogramProof: 30. Application ExampleABCD is a quadrilateral as shown below, solve for x5x 50662x – 30527. Application ExampleIf m 1 m 2 m 3, then ABCD is a parallelogramA1B231. Application ExampleABCD is a parallelogram, if DF BE, then AECF is alsoa parallelogramEAB3DCDCF28. Application ExampleABCD is a quadrilateral as shown below, solve for x3x – 2050o60o60o50o2x 10Mr. Lin4
Geometry WorksheetQuadrilaterals32. Congruent & Parallel Opposite SidesIf one pair of opposite sides of a quadrilateral are bothcongruent and parallel, then the quadrilateral is aparallelogramGiven: If AB CD , and AB CDProve: ABCD is a parallelogramProof: Section:Name:35. Congruent Opposite AnglesIf both pairs of opposite angles of a quadrilateral arecongruent, then the quadrilateral is a parallelogramGiven: A C, and B DProve: ABCD is a parallelogramProof:33. Application ExampleABCD is a quadrilateral as shown below, solve for x and y.x 5y 5036. Application ExampleABCD is a quadrilateral, solve for x30o10x 301030o130o50o2y – 2050o130o2x – 40534. Application ExampleABCD is a parallelogram, if m 1 m 2, then AECF isalso a parallelogramEA37. Application ExampleIf m 1 m 2 m 3, then ABCD is a parallelogram.1AB4B132DDC2CFMr. Lin5
Geometry WorksheetQuadrilaterals38. Bisecting DiagonalsIf the diagonals of a quadrilateral bisect each other, thenthe quadrilateral is a parallelogramGiven: AC and BD bisect each other at OProve: ABCD is a parallelogramProof: Section:Name:41. Application ExampleABCD is a quadrilateral, solve for x.2xo 80o3xo100o–2xo2(xo 45o)–10ooReview: proving quadrilaterals are parallelograms:(A)(B)(C)(D)39. Application Example AOB COD, then ABCD is a parallelogram(E)AB(F)ODC40. Supplementary Consecutive AnglesIf an angle of a quadrilateral is supplementary to both ofits consecutive angles, then the quadrilateral is aparallelogramGiven: A and B are supplementary, and A and D are supplementaryProve: ABCD is a parallelogramProof:Mr. Lin6
Geometry WorksheetQuadrilateralsSection:Name:47. Proving Rectangles:Do Now:42. List the Properties/Theorems of Parallelograms(1)(1)(2)(2)(3)(4)(5)(3)48. Theorem: If one angle of a parallelogram is a rightangle, then the parallelogram is a rectangleGiven: ABCD is a parallelogram and m A 90AProve: ABCD is a rectangleRectanglesDBC43. Write the definition of rectangle:.44. Theorem: All angles of a rectangle are right anglesGiven: ABCD is a rectangle with A 90oProve: B 90 o, C 90 o, D 90 oAD45. Theorem: The diagonals of a rectangle are congruentGiven: ABCD is a rectangleAProve: AC BDD B49. Theorem: If a quadrilateral is equiangular, it is arectangleGiven: ABCD is a quadrangular & m A m B m CA m DProve: ABCD is a rectangleCBC 46. Properties of Rectangle:(1)CD50. Theorem: The diagonals of a parallelogram arecongruentAGiven: AC BDProve: ABCD is a rectangleD 51. Application Example: ABCD is a parallelogram, m A 6x - 30 and m C 4x 10. Show that ABCD is arectangle(2)(3)Mr. LinB7BC
Geometry WorksheetQuadrilateralsSection:Name:Rhombuses57. Proving Rhombuses:52. Write the definition of rhombuses:(1).(2)53. Theorem: All sides of a rhombus are congruentGiven: ABCD is a rhombus with AB DA AProve: AB BC CD DABD 58. Theorem: If a parallelogram has two congruentconsecutive sides, then the parallelogram is a rhombusGiven: ABCD is a parallelogram and AB DAProve: ABCD is a rhombusA 54. Theorem: The diagonals of a rhombus are perpendicularto each otherAGiven: ABCD is a rhombusProve: AC BDD (4)C (3) B DC59. Theorem: If a quadrilateral is equilateral, it is arhombusGiven: ABCD is a parallelogram and AB BC CD DAAProve: ABCD is a rhombusC D BBC60. Theorem: If the diagonals of a parallelogram areperpendicular, it is a rhombusBAGiven: AC BDProve: ABCD is a rhombusD 55. Theorem: The diagonals of a rhombus bisect its anglesAGiven: ABCD is a rhombusProve: AC bisects DAB and DCBBD bisects CDA and CBAD BCC 61. Theorem: If each diagonal of a parallelogram bisectstwo opposite angles, then it is a rhombusGiven: AC bisects DAB and DCBBABD bisects CDA and CBAProve: ABCD is a rhombus DC62. Application Example:ABCD is a parallelogram. AB 2x 1, DC 3x - 11,BAD x 13AProve: ABCD is a rhombusDC56. Properties of Rhombuses:(1)(2)63. Application Example:ABCD is a parallelogram, AB 3x - 2, BC 2x 2, andCD x 6. Show that ABCD is a rhombus.(4)Mr. LinBA(3)DC8
Geometry WorksheetQuadrilateralsASection:Name:BSquares64. Write the definition of squares:D.C.65. Properties of Squares:(1)(2)(3)66. Proving Squares:(1)(2)67. Application Example:ABCD is a square, m A 4x - 30, AB 3x 10 and BC 4y. Solve x and y.Mr. Lin9
Geometry Worksheet Quadrilaterals Section: Name: Mr. Lin 6 38. Bisecting Diagonals If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram Given: AC and BD bisect each other at O .
