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State whether the given statement is true or false:

In the given figure, AD and BE are the medians of Δ ABC and DF || BE. Then $C F = 13 A C$ .

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True

False

answer is B.

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Detailed Solution

Given AD and BE are the medians of Δ ABC and DF || BE.
Let us look at the figure of

Δ A B C

Δ A B C

A C = A E + E C

A E = E C

… (E is the midpoint of AC)

A C = 2 E C

... (i)
In

Δ B E C

, DF||BE.
Also, by midpoint theorem D is the midpoint of BC.
EC= EF + CF
Since, EF = CF.
EC = 2CF … (ii) From equation (i) and (ii) we have,
AC = 4CF

C F = 14 A C

The given statement is false.
When AD and BE are the medians of ΔABC and DF || BE.
Then

C F = 14 A C

.
Hence, 2 is the correct option.

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