Question

ABCD is a parallelogram and E is the midpoint of side BC, DE and AB when produced to meet F. Prove that AF = 2AB .

Answer 1

Answer:

proved

Explanation:

ΔEBF congruent to ΔECD

( By AAS Similarity)

Therefore,

BF = CD

Now,

AF = AB + BF

= AB + CD

= AB + AB

AF = 2AB

Answer 2

Answer:

Explanation:

In the figure

△DCE and BFE

any DEC = any BEF (vertically opposite angles)

EC=BE (E is the mid point)

∠DCB=∠EBF (alternate angle since DC parallel to AF)

So △DCE congruent to △BFE (AAS)

Therefore DC=BF (1)

now CD = AB (Since ABCD is a parallelogram)  

So AF=AB+BF

=AB+DC from (1)

=AB+AB  

=2AB

Thus proven.