SOLUTION: Give a detailed proof of the following fact: The line segment joining the midpoints of two sides of a triangle is parrallel to and half the length of the third side.

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Question 197026: Give a detailed proof of the following fact: The line segment joining the midpoints of two sides of a triangle is parrallel to and half the length of the third side.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

I'll let you fill in the details, but here is the strategy:

Given triangle ABC, P the midpoint of AB, Q the midpoint of BC.

Since angle B is angle B and PB:AB = BQ:BC = 1:2 by definition of midpoint, then ABC is similar to PBQ.

Use the fact that angle BPQ = angle BAC by similarity of ABC and PBQ and one of the theorems about parallel lines and a transversal to prove that PQ parallel to AC.

Then use proportionality of the sides of similar triangles to show that if PB:AB = BQ:BC = 1:2 by definition of midpoint, then PB:AB = BQ:BC = PQ:AC = 1:2.

John