1. In the adjoining figure, BD is a diagonal of quad. ABCD. Show that ABCD is a parallelogram and calculate the area of Igm ABCD. (Hint. AB || DC (why ?) and AB = DC.)
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Answer:
Step-by-step explanation:
Given: The diagonal BO of parallelogarn ABCD intersects the segment AE at F,
where E is any point on BC.
To prove: DF x EF= FB x FA
Proof: In triangles AFD and BFE,
∠FAD = ∠FEB (Alternate angles)
∠AFD = ∠BFE (Vertically opposite angles)
Therefore △ADF ~ △BFE (AA similarity)
DF/FA = FB/EF
Hence DF x EF = FB x FA
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