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November 17th, 2015, 11:15 AM  #1 
Newbie Joined: Jul 2011 Posts: 4 Thanks: 0  Simple(?) proof on points on bisecting lines.
Hey all, I'm an adult going back through geometry (the McDougal text). Only in chapter 4, but it's going smoothly. However, there's one particular problem that is tripping me up  it seems like I'm supposed to assume something that isn't necessarily true. Either that or I'm missing the obvious, but I've asked some other people and they don't see anything either. Any help would be very appreciated . 
November 17th, 2015, 01:29 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,089 Thanks: 1902 
Choose F on BD extended, G on BE extended and H on DE so that $\angle$DFP = $\angle$DHP = $\angle$EGP = 90°. As triangles PFD, PHD are congruent, PF = PH. As triangles PGD, PHD are congruent, PG = PH. Hence PF = PG, and so triangles PFB, PGB are congruent, which implies that $\angle$PBF = $\angle$PBG, i.e. that BP bisects $\angle$ABC. 
November 17th, 2015, 07:49 PM  #3  
Newbie Joined: Jul 2011 Posts: 4 Thanks: 0  Quote:
Last edited by skipjack; November 17th, 2015 at 08:51 PM.  

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bisecting, lines, points, proof, simple 
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