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 :
Let we have a parallelogram ABCD , and E and F are mid points of AB and CD respectively . We form our diagram , As :
Here Diagonals AC and BD and EF intersect at " O " .
We know diagonals of parallelogram bisect each other , So
AO = CO
In ABC , we have
AE = BE , as we assumed E is mid point of AB
And
AO = CO , from property of parallelogram .
SO,
From conserve of mid point theorem , we get
EO | | BC , SO
EF | | BC ( As EO is part of line EF )
And
We know BC | | DA , from property of parallelogram , So
We can say
BC | | DA | | EF
So,
Joining the mid points of the opposite sides of a parallelogram are parallel to the other pairs of parallel sides. ( Hence proved )
Let we have a parallelogram ABCD , and E and F are mid points of AB and CD respectively . We form our diagram , As :
Here Diagonals AC and BD and EF intersect at " O " .
We know diagonals of parallelogram bisect each other , So
AO = CO
In ABC , we have
AE = BE , as we assumed E is mid point of AB
And
AO = CO , from property of parallelogram .
SO,
From conserve of mid point theorem , we get
EO | | BC , SO
EF | | BC ( As EO is part of line EF )
And
We know BC | | DA , from property of parallelogram , So
We can say
BC | | DA | | EF
So,
Joining the mid points of the opposite sides of a parallelogram are parallel to the other pairs of parallel sides. ( Hence proved )