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Example 4 - In figure, ABCD is a quadrilateral and BE - Triangles with same base & same parallel lines

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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)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.