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Question
D and F are midpoints of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E.
- Prove that BDFE is a parallelogram
- Find AB, if EF = 4.8 cm.
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Solution
The required figure is shown below
(i) Since F is the midpoint and EF || AB.
Therefore E is the midpoint of BC.
So, `BE = 1/2BC and EF = 1/2AB` …..(1)
Since D and F are the mid-points of AB and AC
Therefore DE || AC.
So, `DF = 1/2BC and DB = 1/2"AB"` …..(2)
From (1), (2) we get
BE = DF and BD = EF
Hence BDEF is a parallelogram.
(ii) Since
AB = 2EF
= 2 × 4.8
= 9.6 cm.
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