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The line segment joining the mid-points ...

The line segment joining the mid-points of any two sides of a triangle is parallel to the third side of a triangle.

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GIVEN `A Delta ABC ` in which D and E are the midpoint of AB and AC respectively
TO PROVE `AE||EC`.

PROOF Since D and E are the midpoints of AB and AC resepctively, we have AD=DB and AE=EC.
`:. (AD)/(DB)=(AE)/(EC)` [ each equal to 1]
Hence, by the converse of Thale's theorem , `DE||BC`.
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