Geometry Worksheet Quadrilaterals Section: Name:

Transcription

1 o Now: Write the definition of quadrilaterals: 9. The notation of parallelogram:.. Parts & Properties of the Quadrilaterals P Q Name the parallelogram and show its parallel sides: S R 1. : Vertices that are endpoints of the same side. 2. : Sides that have a common endpoint. 3. : Sides that do not have a common endpoint. Theorems of Parallelogram 10. Theorem of ividing iagonals diagonal divides a parallelogram into two congruent triangles Given: is a parallelogram Prove: 4. : ngles whose vertices are consecutive. 5. : ngles whose vertices are not consecutive. 6. : line segment whose endpoints are two nonadjacent vertices of the quadrilateral. 7. The sum of the measures of the angles of a quadrilateral is: 11. Theorem of pposite Sides pposite sides of a parallelogram are congruent Given: is a parallelogram Prove:. Parallelograms 8. Write the definition of parallelogram:. Mr. Lin 1

2 onow: 15. is a parallelogram, is a parallelogram, if is a parallelogram, what s the perimeter of? = 3, = 4 = 6, + =? 12. Theorem of pposite ngles pposite angles of a parallelogram are congruent, and Given: is a parallelogram Prove:, and y + 2 3x - 3 x + 7 2y is a parallelogram, if = x+4, = 2y-6, = 3x-4, an = y+2, solve for x and y. x+4 3 y+2 6 2y 6 4 3x is a parallelogram, what are the values of x and y? x + 20 o y 20 o 17. Theorem of onsecutive ngles The consecutive angles of a parallelogram are supplementary Given: is a parallelogram Prove: and are supplementary and are supplementary and are supplementary and are supplementary 180 o y 2x 60 o 14. Theorem of isecting iagonals The diagonals of a parallelogram bisect each other Given: is a parallelogram Prove: and bisect each other at 18. is a parallelogram, what are the values of x, y and z? 120 o x o z o y o Mr. Lin 2

3 19. is a parallelogram, what are the values of x and y? x+30 o x 30 o 23. Given: is a parallelogram, Prove: E F E y +20 o F 20. is a parallelogram, calculate the perimeter of? x y 10 y x Given: is a parallelogram, F E Prove: F E E 21. is a parallelogram, solve for x. F x+30 x 10 x+10 2x 22. Given: is a parallelogram Prove: X Y X Review: Theorems of Parallelogram Y Mr. Lin 3

4 Prove Quadrilaterals are Parallelograms 25. List the criteria for proving quadrilaterals are parallelograms: () () 29. ongruent pposite Sides If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram Given: If, and Prove: is a parallelogram () () (E) (F) 26. Parallel pposite Sides If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram Given: If, and Prove: is a parallelogram 30. pplication Example is a quadrilateral as shown below, solve for x 6 x x pplication Example If m 1 = m 2 = m 3, then is a parallelogram pplication Example is a parallelogram, if F = E, then EF is also a parallelogram E F 28. pplication Example is a quadrilateral as shown below, solve for x 50 o 60 o 3x 20 2x o 50 o Mr. Lin 4

5 32. ongruent & Parallel pposite Sides If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram Given: If, and Prove: is a parallelogram 35. ongruent pposite ngles If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Given:, and Prove: is a parallelogram 33. pplication Example is a quadrilateral as shown below, solve for x and y o y + 50 x + 5 2y o pplication Example is a quadrilateral, solve for x x o 50 o 50 o 2x o 34. pplication Example is a parallelogram, if m 1 = m 2, then EF is also a parallelogram 1 F E pplication Example If m 1 = m 2 = m 3, then is a parallelogram Mr. Lin 5

6 38. isecting iagonals 41. pplication Example If the diagonals of a quadrilateral bisect each other, then is a quadrilateral, solve for x. the quadrilateral is a parallelogram Given: and bisect each other at Prove: is a parallelogram 3x o 2x o +80 o 2(x o +45 o ) 10 o o 100 o 2x o Review: proving quadrilaterals are parallelograms: () () () 39. pplication Example, then is a parallelogram () (E) (F) 40. Supplementary onsecutive ngles If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram Given: and are supplementary, and and are supplementary Prove: is a parallelogram Mr. Lin 6

7 o Now: 42. List the Properties/Theorems of Parallelograms _ (4) (5) Rectangles 43. Write the definition of rectangle:. 47. Proving Rectangles: 48. Theorem: If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle Given: is a parallelogram and m = 90 Prove: is a rectangle 44. Theorem: ll angles of a rectangle are right angles Given: is a rectangle with = 90 o Prove: = 90 o, = 90 o, = 90 o 49. Theorem: If a quadrilateral is equiangular, it is a rectangle Given: is a quadrangular & m = m = m = m Prove: is a rectangle 45. Theorem: The diagonals of a rectangle are congruent Given: is a rectangle Prove: 50. Theorem: The diagonals of a parallelogram are congruent Given: Prove: is a rectangle 46. Properties of Rectangle: 51. pplication Example: is a parallelogram, m = 6x - 30 and m = 4x Show that is a rectangle Mr. Lin 7

8 Rhombuses 52. Write the definition of rhombuses: 53. Theorem: ll sides of a rhombus are congruent Given: is a rhombus with Prove: 57. Proving Rhombuses: (4) 58. Theorem: If a parallelogram has two congruent consecutive sides, then the parallelogram is a rhombus Given: is a parallelogram and Prove: is a rhombus 54. Theorem: The diagonals of a rhombus are perpendicular to each other Given: is a rhombus Prove: 59. Theorem: If a quadrilateral is equilateral, it is a rhombus Given: is a parallelogram and Prove: is a rhombus 60. Theorem: If the diagonals of a parallelogram are perpendicular, it is a rhombus Given: Prove: is a rhombus 55. Theorem: The diagonals of a rhombus bisect its angles Given: is a rhombus Prove: bisects and bisects and 61. Theorem: If each diagonal of a parallelogram bisects two opposite angles, then it is a rhombus Given: bisects and bisects and Prove: is a rhombus 62. pplication Example: is a parallelogram. = 2x + 1, = 3x - 11, = x + 13 Prove: is a rhombus 56. Properties of Rhombuses: 63. pplication Example: is a parallelogram, = 3x - 2, = 2x + 2, and = x + 6. Show that is a rhombus. (4) Mr. Lin 8

9 Squares 64. Write the definition of squares: 65. Properties of Squares: 66. Proving Squares: 67. pplication Example: is a square, m = 4x - 30, = 3x + 10 and = 4y. Solve x and y. Mr. Lin 9