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Question
The alongside figure shows a parallelogram ABCD in which AE = EF = FC.
Prove that:
- DE is parallel to FB
- DE = FB
- DEBF is a parallelogram.
Solution
Construction:
Join DF and EB
Join diagonal BD
Since diagonals of a parallelogram bisect each other.
∴ OA = OC and OB = OD
Also, AE = EF = FC
Now, OA = OC and AE = FC
⇒ OA - AE = OC - FC
⇒ OE = OF
Thus, in quadrilatreal DEFB, bisect each other.
OB = OD and OE = OF
⇒ Diagonals of a quadrilateral DEFB bisect each other.
⇒ DEFB is a parallelogram.
⇒ DE is parallel to FB
⇒ DE = FB ...(Opposite sides are equal)
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