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

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.