What is Parallelogram: Definition and 126 Discussions

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.
By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English.
The three-dimensional counterpart of a parallelogram is a parallelepiped.
The etymology (in Greek παραλληλ-όγραμμον, parallēl-ógrammon, a shape "of parallel lines") reflects the definition.

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  1. J

    Finding the center of mass of a piecewise function

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  4. N

    Proof Involving the Diagonals of Parallelogram

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  5. S

    MHB Need help with parallelogram proof

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  6. A

    MHB Calculating Perimeter & Area of a Parallelogram & Triangle

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  7. anemone

    MHB Parallelogram ABCD: Finding AC from PB & PD

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  8. M

    I PDEs: Laplace's Equation over a Parallelogram

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  9. C

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  10. Robin04

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  11. Akash47

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  12. S

    MHB Parallelogram with diagonals. Need to find the area (S).

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  13. T

    B Trig Problem Altitudes of Parallelogram

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  14. DLeuPel

    B Understanding the Parallelogram Method for Solving Forces

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  15. Z

    MHB How to Calculate the Diagonal Length of a Parallelogram?

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  16. Monoxdifly

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  17. Richie Smash

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  18. Z

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  19. S

    I Solving Confusion About Parallelograms in Curved Spacetime

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  20. A

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  21. N

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  22. I

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  23. karush

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  24. M

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  25. M

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  27. M

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  30. J

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  32. S

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  33. Julian102

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  35. T

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  36. A

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  37. B

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  38. B

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  39. R

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  40. F

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  41. J

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  42. Z

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  43. L

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  44. Z

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  45. T

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  46. karush

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  47. U

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  48. Albert1

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  49. S

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  50. W

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