Question

guys plz answer this question


on paper

the correct one will get a brainliest .....

Thanx in advance

Answer 1

Hi !

ABCD is a parallelogram. AC and BD are the diagonals of the parallelogram ABCD. E and F are the centroid of ΔABD and ΔBCD respectively.

We know that, diagonals of a parallelogram bisect each other.

Therefore, AO and CO are the medians of ΔABD and ΔBCD respectively. E and F lies on AC.

The centroid of a triangle divides the medians in the ratio of 2:1.

∴$\frac{AE}{OE}$ =$\frac{2}{1}$

⇒ AE = 2OE ...............(1)

$\frac{CF}{OF}$ =$\frac{2}{1}$

⇒ CF = 2OF.................(2)

Adding (1) and (2) we get

AE + CF = 2OE + 2OF

⇒ AE + CF = 2(OE + OF) = 2EF ...........(3)

AO = CO

⇒$\frac{2}{3}$AO = $\frac{2}{3}$CO .............(4)

From (3) and (4), we get:

AE + AE = 2EF

⇒ 2 AE = 2 EF

⇒ AE = EF 

Therefore (A) AE option is correct.

Hope this may help you.

Answer 2

See the diagram.
Answer EF = AE.
A median is divided in ratio 2:1 by the centroid. See picture for detailed steps.