SOLUTION: Triangle ABC with vertices (-J,0) (0,K) (L,0) and midpoints M,N,and O of the line segments Ab, BC, and AC. Prove the perimeter of triangle MNO is one half the perimeter of triangl

Algebra ->  Geometry-proofs -> SOLUTION: Triangle ABC with vertices (-J,0) (0,K) (L,0) and midpoints M,N,and O of the line segments Ab, BC, and AC. Prove the perimeter of triangle MNO is one half the perimeter of triangl      Log On


   

Question 1082718: Triangle ABC with vertices (-J,0) (0,K) (L,0) and midpoints M,N,and O of the line segments Ab, BC, and AC.
Prove the perimeter of triangle MNO is one half the perimeter of triangle ABC.
Answer by solver91311(24713) About Me  (Show Source):
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Coordinates of midpoints (M, N, and O) derived from the midpoint formulas. Verification left as an exercise for the student.












Similarly,

and


But the perimeter of is the sum

And the perimeter of is the sum and:



Q.E.D

John

My calculator said it, I believe it, that settles it