Question

prove that the straight lines joining the mid points of the opposite sides of a parallelogram are parallel to the other pairs of parallel sides

Answer 1

ABCD is a parallelogram and E and F are mid points of AB and CD .

Diagonals AC and BD and EF intersect at  "  O  " .  We know diagonals of parallelogram bisect each other  , So

AO  =  CO  

In ∆ ABC  ,

AE  =  BE  ( E is mid point of AB )

AO =  CO , (property of parallelogram .)

SO,

From conserve of mid point theorem , we get

EO  | | BC  , SO

EF  | | BC                          ( As EO is part of line EF )

We know BC  | | DA  (from property of parallelogram) ,

therefore:--

BC  | | DA  | | EF 

Hence : It is proved that ,

Joining the mid points of the opposite sides of a parallelogram are parallel to the other pairs of parallel sides.

Answer 2

Answer:

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