Math CentralQuandaries & Queries


Question from Manis, a student:
Prove that the line joining the midpoint of two sides of a triangle
is parallel to the third and half of it.


Call the vertices A, B, and C (these are vectors)

The midpoint of the segment XY is (X+Y)/2 (also a vector).

The vector expressing the length and direction of the side is (Y-X). (This is a "free vector" that represents a difference of locations, not a location).\

Use this to answer the question.

Good Hunting!

PS: Then for an encore use the same tools to show that the midpoints of the edges of any quadrilateral ABCD form the vertex set of a parallelogram. Have fun!


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