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In the given figure, ABCD is a ||gm and ...

In the given figure, ABCD is a ||gm and E is the mid-point of BC. Also, DE and AB when produced meet at F. Then.

A

`AF=(3)/(2)AB`

B

`AF=2AB`

C

`AF=3AB`

D

`AF^(2)=2AB^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
In `angle EDC and angle EFB`, we have
`angle DCE= angle EBF " "("alt. interior " angle),`
` angle DEC= angle FEB " " ("vert. opp. "angle)`
` and EC=EB.`
`therefore triangle EDC ~=triangle EFB " and therefore, "BF=DC.`
`therefore AF=(AB+BF)=(AB+DC)=2AB.`
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