Prove that the line segment joining the mid points of two side of a triangle is parallel to the third side and equal to half of it.

Explanation

Suppose `A` be the origin and `AB=vecb` and `AC=vecc`.

Let `D` and `E` be the mid points on `AB` and `AC` respectively.

`implies vec{AD}={vecb}/2, vec{AE}={vecb}/2`

`implies vecDE` is parallel to `frac{vecb-vecc}{2}` or `vecb-vecc`

And `vec{BC}` is parallel to `vecb-vecc`

`implies vec{DE}` is parallel to `vec{BC}`

And `|vec{DE}|=frac{|vecb-vecc|}{2}, |vec{BC}|=|vecb-vecc|`

`implies |vec{DE}|=frac{|vec{BC}|}{2}`

...