Question

in a parallelogram abcd k is the midpoint of side CD and DM is drawn parallel to BK which meet CB produce at m and cut side Ab at l prove that ad =1/2cm

Answer 1

Opposite Sides of Parallelogram are Equal

Explanation:

The midpoint of CD is 'k'

So, $CK = \frac {1}{2}CD$

$\frac {CK}{CD} = \frac {CB}{CM} = \frac {BK}{DM}$ ""(1)

$\frac {CK}{CD} = \frac {CB}{CM}$

$\frac {1}{2} = \frac {CB}{CM}$

$CB = \frac {1}{2} CM$

$AD = \frac {1}{2}$  CM (AD = CB, Opposite Sides of parallelogram)

Hence Proved !

From (1)

$\frac {CK}{CD} = \frac {BK}{DM}$

$\frac {1}{2} = \frac {BK}{DM}$

DM = 2 BK

Hence Proved !