Angle-bisector ProofDate: 10/16/97 at 14:46:12 From: Tim Subject: Geometry Dear Dr. Math, Prove that in a triangle ABC, a pair of angle-bisectors cannot be perpendicular. I have absolutely no idea what this is even about. Haven't done geometry in 15 years! Yours truly, Tim in Montreal Date: 10/16/97 at 15:47:35 From: Doctor Wilkinson Subject: Re: Geometry Draw a picture! Suppose the bisector of the angle at A and the bisector of the angle at B are perpendicular. Suppose they intersect at D. This gives you a smaller triangle ABD, where the angle at D is a right angle. That tells you that the angle DAB and the angle DBA add up to 90 degrees, because the angles of a triangle always add up to 180 degrees. That means that the angle CAB, which is twice DAB (because AD is the angle bisector; and the angle CBA, which is twice DBX (Because BD is the angle bisector), add up to twice 90 degrees, or 180 degrees. But that's impossible, because all three angles of the triangle have to add up to 180 degrees, and there's nothing left. -Doctor Wilkinson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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