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Medially Similar (Posted on 2005-08-19) Difficulty: 2 of 5
Let ABC be a triangle, with M the midpoint of BC, and DEF a triangle, with N the midpoint of EF. Suppose that angle BAM equals angle EDN and angle CAM equals angle FDN. Show that triangles ABC and DEF are similar.

See The Solution Submitted by McWorter    
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Solution A different way | Comment 2 of 3 |
A different way to prove this is showing that if AM=DN, then both triangles are identical.

To show this, it suffices to prove that given A, M, and the angles BAM and CAM, B and C are uniquely defined.

Consider a central symmetry, with center M. B and C are symmetric to each other. The symmetric line to AB intersects AC at C, and this is unique, so B is unique too.

  Posted by Old Original Oskar! on 2005-08-19 17:39:53
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