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

# 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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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.