Q. 75.0( 2 Votes )

In ΔABC, a line parallel to , passes through the mid-point of . Prove that the line bisects .

Answer :


Given: In ∆ABC, a line parallel to BC, passes through the mid-point of AB.


To prove: Line m bisects AC.


Proof: In the plane of ∆ABC, line m is parallel to BC and intersects AB at a point other than a vertex of the triangle.


Thus, m intersects AC.


Let m AC = {E}


In ∆ABC, D is the mid-point of AB.


AD = DB



In ∆ABC, A-D-B, A-E-C and DE||BC.




AE = EC and A-E-C.


E is the mid-point of AC.


Thus, line m bisects AC.


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