Question:
The sides AB and CD of a parallelogram ABCD are bisected at E and F. Prove that EBFD is a parallelogram.
Solution:
Since ABCD is a parallelogram
∴ AB ∥ DC and AB = DC
⇒ EB ∥ DF and (1/2) AB = (1/2) DC
⇒ EB ∥ DF and EB = DF
EBFD is a parallelogram.
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