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Ishita Katyal
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Asked: 2020-11-03T09:56:22+00:00 In:

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.

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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:164
Questions No:15

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
      Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.

      ar(AOD) = ar(BOC) [∵ Given]
      adding ar(AOB) both of sides
      ar(AOD) + ar(AOB) = ar(BOC) + ar(AOB)
      ⇒ ar(ABD) = ar(ABC)
      ΔABC and ΔABC are on the same base AB and ar(ABD) = ar(ABC).
      Therefore, AB ∥ DC
      [∵ Triangles on the same base (or equal bases) and having equal areas lie between

      the same parallels.]
      Hence, ABCD is a trapezium.

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