Math, asked by mayankshekhar, 10 months ago

In a parallelogram ABCD K is the mid point
of side CD and DM is drawn Parallel to BK,
which meets CB Produced at M and cut side
AB at L. Prove that ADF = 1/2 CM.

Answers

Answered by bhagyashreechowdhury

If K is the mid point of side CD and DM is drawn parallel to BK, which meets CB produced at M and cut side AB at L then AD = 1/2 CM is proved below.

Step-by-step explanation:

Referring to the figure attached below the question is solved as follows:

Step 1:

In ∆ DCM, we are given

K is a midpoint of side CD and DM // BK

Since we know that, in a triangle, the line-segment joining the midpoints of any two sides will be parallel to the third side and half its length, therefore we can conclude that

B is also the midpoint of side CM

And,

CB = BM = ½ CM …… (i)

Step 2:

ABCD is given to be a parallelogram.

And we know that the opposite facing sides of a parallelogram are equal in length, therefore, we get

AD = CB ……. (ii)

Now, from (i) & (ii), we get

AD = ½ CM

Hence proved

Hope this is helpful!!!!!

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Answered by routgitanjali026