Question

D. C E In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB. A B

It is very urgent​

Answer 1

Step-by-step explanation:

Solution

In given figure ABCD is a parallelogram.

Here, E is midpoint of BC. So, BE=CE.

⇒ Consider △CDE and △BFE

⇒ BE=CE [Given]

⇒ ∠ CED= ∠ BEF [Vertically opposite angles]

⇒ ∠ DCE= ∠ FBE [Alternate angles]

⇒ △CDE≅△BFE [By ASA criteria]

⇒ So, CD=BF [CPCT] --- ( 1 )

⇒ But, CD=AB ---- ( 2 )

⇒ AB=BF [From ( 1 ) and ( 2 )] --- ( 3 )

⇒ AF=AB+BF

⇒ AF=AB+AB [From ( 3 )]

∴ AF=2AB