Theorem 8.9 - Class 9 - Line joining mid-points of 2 sides of triangle

Theorem 8.9 - Chapter 8 Class 9 Quadrilaterals - Part 2
Theorem 8.9 - Chapter 8 Class 9 Quadrilaterals - Part 3

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Theorem 8.9 The line segment joining the mid-points of two sides of a triangle is parallel to the third side. Given : ABCD is a triangle where E and F are mid points of AB and AC respectively To Prove : EF BC Construction : Through C draw a line segment parallel to AB & extend EF to meet this line at D. Proof : Since EB DC with transversal ED. AEF = CDF In AEF and CDF AEF = CDF AF = CF AFE = CFD AEF CDF So, EA = DC But, EA = EB Hence, EB = DC Now, In EBCD, EB DC & EB = DC Thus, one pair of opposite sides is equal and parallel. Hence EBCD is a parallelogram. Since opposite sides of parallelogram are parallel. So, ED BC i.e. EF BC Hence, proved.

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.