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Ishita Katyal
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Asked: 2020-11-03T09:53:55+00:00 In:

ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).

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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:13

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
      ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).

      Construction: Join CX.
      Triangles ADX and ACX are on the same base AX and between same parallels AB ∥ DC.
      Hence, ar(ADX) = ar(ACX) …(1)
      [∵ Triangles on the same base (or equal bases) and between same parallels are equal in area.]
      Similarly, triangles ACY and ACX are on the same base AC and between same parallels AC ∥ XY.
      Hence, ar(ACY) = ar(ACX) …(2)
      From the equation (1) and (2), ar(ADX) = ar(ACY).

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