Prove that the straight line joining the mid-points of the oblique sides of a
trapezium is parallel to each of the parallel sides. draw the figure also
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Here, AB∣∣DC
M and N are the mid points of sides AD and BC respectively.
MN is joined.
To prove : MN∣∣AB or DC.
Produce AD and BC to meet at P.
Now, In △PAB
DC∣∣AB
DA
PD
=
CB
PC
2PM
PD
=
2CN
PC
M and N are midpoints of AD and BC respectively.
PM
PD
=
CN
PC
MN∣∣DC But DC∣∣AB
Therefore, MN∣∣DC∣∣AB
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