Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = 1/4 ar(ABC).

Q : 2      In a triangle ABC, E is the mid-point of median AD. Show that     \small ar(BED)=\frac{1}{4}ar(ABC).
 

Answers (1)

best_answer

We have a triangle ABC and  AD is a median. Join B and E.

Since the median divides the triangle into two triangles of equal area.
\therefore ar(\DeltaABD) = ar (\DeltaACD) = 1/2 ar(\DeltaABC)..............(i)
Now, in triangle \DeltaABD,
BE is the median [since E is the midpoint of AD]
\therefore ar (\DeltaBED) = 1/2 ar(\DeltaABD)........(ii)

From eq (i) and eq (ii), we get

ar (\DeltaBED) = 1/2 (1/2 ar(ar (\DeltaABC))
ar (\DeltaBED)  = 1/4 ar(\DeltaABC)

Hence proved.

Posted by

manish

View full answer

Similar Questions

Trending Articles/News

anam-khan

Board Exam Date 2025 Live: Bihar Class 10, 12 model papers out, time table soon; updates on CBSE, UP

Latest Question