In ABC- medians AD -BE and CF are drawn on sides BC - AC and AB respectively and ADC - BEC- What can you say about ABC -A- right angledB- right angled isoscelesC- equilateralD- isosceles

The correct option is D isosceles Given ADC ∼ BEC AD BE= AC BC= DC EC 2EC 2DC= DC ECex (since D and E are mid points of BC and AC) EC DC = DC ECex ⇒ EC=DC If ...

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Standard X

Mathematics

Similar Triangles

In ABC, media...

Question

In $△ A B C$ , 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 $△ A B C$ ?

equilateral

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isosceles

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right angled

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right angled isosceles

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Solution

The correct option is B
isosceles

Given $△ A D C \sim △ B E C$
$\frac{A D}{B E} = \frac{A C}{B C} = \frac{D C}{E C}$
$\frac{2 E C}{2 D C} = \frac{D C}{E C}$ (since D and E are mid points of BC and AC)
$\frac{E C}{D C} = \frac{D C}{E C} \Rightarrow E C = D C$
If EC = DC $\Rightarrow$ AC = BC
Therefore, $△$ ABC is isosceles with AC = BC

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

The correct option is B isosceles Given △ADC∼△BEC ADBE=ACBC=DCEC 2EC2DC=DCEC (since D and E are mid points of BC and AC) ECDC=DCEC⇒EC=DC If EC = DC ⇒ AC = BC Therefore, △ ABC is isosceles with AC = BC

In $△ A B C$ , 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 $△ A B C$ ?