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E is the mid-point of side AB and F is the mid point of side DC of parallelogram ABCD. Prove that AEFD is a parallelogram.

Rectilinear Figures

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Answer

E is the mid-point of side AB and F is the mid point of side DC of parallelogram ABCD. Prove that AEFD is a parallelogram. Rectilinear Figures, Concise Mathematics Solutions ICSE Class 9.

We know that,

Opposite sides of parallelogram are equal.

∴ AB = CD

⇒ AB2=CD2\dfrac{AB}{2} = \dfrac{CD}{2}

⇒ AE = FD.

Also,

Opposite sides of parallelogram are parallel.

∴ AB || CD

⇒ AE || FD.

∴ AE = FD and AE || FD.

Since, one pair of opposite side of quadrilateral AEFD is parallel.

Hence, proved that AEFD is a parallelogram.

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