March 13th, 2016, 12:08 AM  #1 
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  test for perpendicular lines.
Two lines m and n intersecting at point P are perpendicular if and only if when m is folded onto itself at point P the line n lies on the foldline. Explain. My attempt: When we fold m onto itself at P a foldline forms at P. This foldline is like an axis of reflection symmetry for the line. This implies that the angles formed at P are congruent. Therefore the foldline is perpendicular to line m. Now if line n lies along the foldline it implies line n too is perpendicular to m. Am I correct? Is there a better explanation? Thanks. 
March 13th, 2016, 07:20 PM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
Yep, that's correct 

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lines, perpendicular, test 
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