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8 September, 04:00

AB = 3x

DC = x + 4

AD = y + 2

BC = 2y

Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs.

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  1. 8 September, 05:07
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    see explanation

    Step-by-step explanation:

    If a parallelogram then AB = DC and AD = BC

    Equating AB = DC, then

    3x = x + 4 (subtract x from both sides)

    2x = 4 (divide both sides by 2)

    x = 2

    Thus

    AB = 3x = 3 (2) = 6 and DC = x + 4 = 2 + 4 = 6 ⇒ AB = DC

    Equating AD and BC, then

    2y = y + 2 (subtract y from both sides)

    y = 2

    Thus AD = y + 2 = 2 + 2 = 4 and BC = 2y = 2 (2) = 4 ⇒ AD = BC

    Since opposite sides are congruent then ABCD is a parallelogram
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