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D and E are the mid-points of the sides AB and AC respectively of triangle $∆ ABC$ . DE is produced to F. Write an additional information required to prove that CF is equal and parallel to DA.

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FE = EF

DE = CF

DE = EF

DE = RF

answer is C.

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Detailed Solution

Given that, in triangle ABC, D and E are midpoints of AB and AC. DE is produced to F.
Drawing the required figure,
Question Image

We consider triangles

∆ ADE

and

∆ CFE

.
Suppose that

DE = EF

.
Then we have:

AE = CE

(Midpoint)

DE = EF

(Assumed)

∠ AED = ∠ FEC

(Vertically opposite angles)
Thus,

∆ ADE ≅ ∆ CFE

.
Now, we know that:

AD = CF

∠ ADE = ∠ CFE

AD = CF

Therefore, the additional information that we need is,

DE = EF

Therefore, option (3) is correct.

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