Theorem 8.10
The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.
Given : ABC where
E is mid point of AB ,
F is some point on AC
& EF BC
To Prove : F is a mid point of AC.
Construction : Through C draw CM AB
Extend EF and let it cut CM at D.
Proof: In quadrilateral EBCD
ED BC
& EB CD
Since both pairs of opposite sides are parallel.
EBCD is a Parallelogram
Since opposite sides of parallelogram are equal.
EB = DC
But, EB = EA
Hence EA = DC
Also,
EB DC
with transversal ED
AEF = CDF
In AEF and CDF
AEF = CDF
AFE = CFD
AE = CD
AEF CDF
So, AF = CD
Hence, F is a mid point of AC
Hence proved.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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