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Question
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.
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Solution
Let us draw a parallelogram ABCD Where F is the midpoint Of side DC and E is the mid-point of side AB of a parallelogram ABCD.
To prove: AEFD is a parallelogram
Proof:
In parallelogram ABCD
AB || DC
BC || AD
AB = DC
`1 /2"AB" = 1/2`DC
AE = DF
Also AD || EF
Therefore, AEFD is a parallelogram.
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