MathematicsIn given figure, if AD=3 cm,AE=5 cm, BD=4 cm,CE=4 cm,CF=2 cm and BF=2.25 cm. then ____.

In given figure, if $AD = 3 cm, AE = 5 cm, BD = 4 cm, CE = 4 cm, CF = 2 cm$ and $BF = 2.25 cm$ . then ____.

Solution:

In given figure, if

AD = 3 cm, AE = 5 cm, BD = 4 cm, CE = 4 cm, CF = 2 cm

and

BF = 2.25 cm

. then

EF | | AB

We know that the line parallel to one side of the triangle that intersects the other two sides in two distinct points then the other two sides of the triangle are divided in the same ratio.
In

ΔABC and ΔEFC

∠ E C F = ∠ A C B

Since,

\frac{CF}{CB} = \frac{2}{2 + 2.5}

\Rightarrow \frac{CF}{CB} = \frac{2}{4.5}

\Rightarrow \frac{CF}{CB} = \frac{4}{9}

Then,

\frac{CE}{EA} = \frac{CF}{CB}

Thus, by SAS similarity

ΔABC \sim Δ EFC

\Rightarrow EF | | AB

Therefore, in the given figure

EF | | AB

In given figure, if $AD = 3 cm, AE = 5 cm, BD = 4 cm, CE = 4 cm, CF = 2 cm$ and $BF = 2.25 cm$ . then ____.

Solution:

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