In $△ A B C$ , the medians AD, BE and CF are drawn on sides BC, AC and AB respectively and $△ A D C \sim △ B E C$ . What can you say about $△ A B C$ ?

isosceles

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right angled

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right angled isosceles

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None of the above

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Solution

The correct option is A
isosceles

Given $△ A D C \sim △ B E C$
$\frac{A D}{B E} = \frac{A C}{B C} = \frac{D C}{E C} . . . . (1)$

$\frac{2 E C}{2 D C} = \frac{D C}{E C}$ (since D and E are mid points of BC and AC)

$\frac{E C}{D C} = \frac{D C}{E C} \Rightarrow E C = D C . . . . (2)$
From (1) and (2) ,
$\frac{A C}{B C} = \frac{D C}{D C} \frac{A C}{B C} = 1 \Rightarrow A C = B C$

Therefore, $△ A B C$ is isosceles with AC = BC

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In △ABC, the medians AD, BE and CF are drawn on sides BC, AC and AB respectively and △ADC∼△BEC. What can you say about △ABC?

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In $△ A B C$ , the medians AD, BE and CF are drawn on sides BC, AC and AB respectively and $△ A D C \sim △ B E C$ . What can you say about $△ A B C$ ?