Question

15. In the figure, ABCD is a parallelogram and E is the midpoint of side BC. If
DE and AB when produced meet at F. Prove that AF = 2AB.​

Answer 1

Step-by-step explanation:

Solution :-

in the figure

△DCE and BFE

any DEC = any BEF (vertically opp any)

EC=BE (E is the mid point)

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

So △DCE congruent to △BFE

Therefore DC=BF ...(1)

now CD = AB (ABCD is a parallelogram)

soAF=AB+BF

=AB+DC from (1)

=AB+AB

=2AB