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meph1st0pheles February 6th, 2010 10:58 AM

Geometry Proof
 
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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!

cknapp February 6th, 2010 12:06 PM

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?

pablo February 9th, 2010 12:32 PM

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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