February 6th, 2010, 10:58 AM  #1 
Member Joined: Jan 2010 Posts: 43 Thanks: 0  Geometry Proof
Given Triangle AXB and Triangle AYB are isosceles and share base AB, show that points X,Y, and Z are collinear if and only if Triangle AZB is isosceles with base AB. Attached is the figure. Any help or incite is greatly appreciated. Thanks!

February 6th, 2010, 12:06 PM  #2 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: Geometry Proof
Let C be the midpoint of AB. Draw a line from C to X. Can you show that Y and X both lie on this line? From, there what would triangle AZB need to look like for Z to be on that line?

February 9th, 2010, 12:32 PM  #3 
Newbie Joined: Dec 2009 Posts: 7 Thanks: 0  Re: Geometry Proof
Yes, just check out that the line XY has to be the perpendicular bisector of AB, then any point on it (Z on XY) would meet the condition AZ = BZ


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