Question

ABCD is a parallelogram and E and F are the centroids of triangles ABD and BCD respectively, then EF = 

A. AE 

B. BE 

C. CE 

D. DE

Answer 1

Option : (A)

Given : 

ABCD is a parallelogram 

E and F are the centroids of triangle ABD and BCD 

Since, 

The diagonals of parallelogram bisect each other 

AO is the median of triangle ABD 

And, 

CO is the median of triangle CBD 

EO = \(\frac{1}{3}\)AO 

(Since, centroid divides the median in the ratio 2:1)

Similarly, 

FO = \(\frac{1}{3}\)CO 

EO + FO = \(\frac{1}{3}\)AO +\(\frac{1}{3}\)CO 

= \(\frac{1}{3}\)(AO + CO) 

EF = \(\frac{1}{3}\)AC 

AE = \(\frac{1}{3}\)AO 

= \(\frac{2}{3}\) x \(\frac{1}{2}\) AC 

= \(\frac{1}{3}\)AC 

Therefore, 

EF = AE