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November 17th, 2015, 10:15 AM   #1
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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 .
Attached Images 2015-11-17 12.07.14.jpg (85.5 KB, 7 views) November 17th, 2015, 12:29 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2222 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, 06:49 PM   #3
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Quote:
 Originally Posted by skipjack 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.
Ah, perfect! I had made the altitude from P to BD/BE (your F and G), but I hadn't thought about making an additional one to DE - that was the missing piece. Thanks!

Last edited by skipjack; November 17th, 2015 at 07:51 PM. Tags bisecting, lines, points, proof, simple Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post cacophonyjm Calculus 10 March 12th, 2012 01:14 AM julian21 Algebra 2 November 15th, 2010 03:22 PM Dlarah Algebra 3 June 17th, 2009 01:55 PM temp_tsu Applied Math 1 September 21st, 2008 03:59 PM zomgcopters Calculus 5 October 22nd, 2007 06:43 PM

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