In the fig., AB = CB = CD and EF bisects BD at G. Is it true that G is the midpoint of EF?

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True

False

answer is A.

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Detailed Solution

Given, AB = CB = CD and EF bisects BD at G.
Question Image

From the figure, it is clear that ABCD is a square since, AB = CB = CD.
∠DGE = ∠BGF since, vertically opposite angles are equal.
DG = BG as EF bisects BD at G.
The diagonal BD is a transversal between the parallel lines AB and CD and hence alternate interior angles are equal.
∠GBF = ∠GDE
So,

△ DEG ⩭ △ FBG

[ By ASA congruence rule].
Since, the two triangles are similar, EG = FG.
Hence, G is the midpoint of EF.
So, the given statement is true and the correct option is 1.

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