Question

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

Answer 1

Answer:

Consider △ DEC and △ FEB From the figure we know that ∠ DEC and ∠ FEB are vertically opposite angles ∠ DEC = ∠ FEB ∠ DCE and ∠ FBE are alternate angles ∠ DCE = ∠ FBE It is given that CE = EB By AAS congruence criterion △ DEC ≅ △ FEB DC = FB (c. p. c. t) From the figure AF = AB + BF We know that BF = DC and AB = DC So we get AF = AB + DC AF = AB + AB By addition AF = 2AB Therefore, it is proved that AF = 2AB.

Answer 2

Step-by-step explanation:

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