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Ishita Katyal
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Asked: 2020-11-03T09:54:26+00:00 In:

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

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NCERT Solutions for Class 9 Maths Chapter 9
Important NCERT Questions
Areas of Parallelograms and Triangles
NCERT Books for Session 2022-2023
CBSE Board and UP Board Others state Board
EXERCISE 9.3
Page No:162
Questions No:2

2020-2021areas of parallelograms and trianglescbsechapter 9class 9mathematicsncert
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    1. Get Hindi Medium and English Medium NCERT Solution for Class 9 Maths to download.
      Please follow the link to visit website for first and second term exams solutions.
      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/chapter-9/

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    2. Best Answer
      In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = 1/4 ar (ABC).

      In ΔABC, AD is median. [∵ Given]
      Hence, ar(ABD) = ar(ACD)
      ⇒ ar(ABD) = 1/2 ar(ABC) …(1)
      [∵ A median of a triangle divides it into two triangles of equal areas.]
      Similarly, in ΔABD, BE is medium. [∵ E is the mid-point of AD]
      Hence, ar(BED) = ar (ABE)
      ⇒ ar(BED) = 1/2 ar(ABD)
      ⇒ ar (BED) = 1/2[(1/2)ar(ABC)] [∵ ar (ABD) = (1/2)ar(ABC)]
      ⇒ ar (BED) = 1/4 ar(ABC)

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