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February 6th, 2010, 11:58 AM   #1
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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!
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February 6th, 2010, 01:06 PM   #2
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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?
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February 9th, 2010, 01:32 PM   #3
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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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