in quadrilateral ABCD if a b equal to DC and a be parallel to dc then prove that ABCD is a parallelogram
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BE∥AC
⇒ ABEC is a ∥gm( a pair of oppo. sides are parallel)
ΔABC and ΔACE lie on the same base AC and between the same parallels AC and BE.
∴ ar(ΔABC) = ar(ΔACE)
By adding ar(ΔADC) to both sides
⇒ ar(ΔABC) + ar(ΔADC) = ar(ΔACE) + ar(ΔADC)
⇒ ar(∥gmABCD) = ar(ΔADE)
⇒ ABEC is a ∥gm( a pair of oppo. sides are parallel)
ΔABC and ΔACE lie on the same base AC and between the same parallels AC and BE.
∴ ar(ΔABC) = ar(ΔACE)
By adding ar(ΔADC) to both sides
⇒ ar(ΔABC) + ar(ΔADC) = ar(ΔACE) + ar(ΔADC)
⇒ ar(∥gmABCD) = ar(ΔADE)
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