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Last updated at May 29, 2018 by Teachoo

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Example 4 In figure, ABCD is a quadrilateral and BE ∥ AC and also BE meets DC produced at E. Show that area of Δ ADE is equal to the area of the quadrilateral ABCD. Given: A quadrilateral ABCD where BE ∥ AC To prove: ar (ADE) = ar (ABCD) Proof : We prove ar(ABC) = ar (ACE) & then add ar(ADC) both sides Since, Δ BAC and Δ EAC lie on the same base AC and between the same parallels AC and BE. ∴ ar(BAC) = ar(EAC) Adding ar(ADC) both sides So, ar(BAC) + ar(ADC) = ar(EAC) + ar(ADC) ⇒ ar(ABCD) = ar(ADE)

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.