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Ex 9.3, 4 - In figure, ABC and ABD are two triangles - Median divides triangle into two triangles of equal area

Ex 9.3, 4 - Chapter 9 Class 9 Areas of Parallelograms and Triangles - Part 2

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Question 4 In figure, ABC and ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar(ABC) = ar (ABD). Given: ΔABC and ΔABD on the same base AB & AB bisects CD, i.e. , OC = OD To prove: ar (ABC) = ar (ABD) Proof : In Δ ACD, Since OC = OD ∴ OA is the median. ⇒ ar(Δ AOC) = ar(Δ AOD) Similarly , in Δ BCD Since OC = OD ∴ OB is the median ⇒ ar(Δ BOC) = ar(Δ BOD) Adding (2) & (3) ar(Δ AOC) + ar(Δ BOC) = ar(Δ AOD) + ar(Δ BOD) ar(Δ ABC) = ar(Δ ADB) Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.