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State whether the given statement is true or false:

In Δ ABC, D, E, F are the midpoints of the sides as shown in the figure given below. Then $∠ D F E = ∠ C$ .

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True

False

answer is A.

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Detailed Solution

Given

Δ A B C

such that D, E, F are the midpoints of the sides BC, CA, and AB respectively.
Question Image

Then by the midpoint theorem, as F and E are the midpoints of sides AB and AC,
FE||BC.
Similarly, DE||FB and FD||AC.
Therefore, AFDE, BDEF, and DCEF are all parallelograms.
In parallelogram DCEF,

∠ C = ∠ D F E

. … [opposite angles of a parallelogram are equal]
Hence, the given statement is true.
So, 1 is the correct option.

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