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Unformatted text preview: AD cuts o from BE a segment DE of length precisely 2 AB . Now let AG bisect DE . Then AB = DG = GE ; show that these are also equal to AG . ( Hint: DAE is a right angle.) Conclude that ABG = AGB and GAE = GEA ; use this to show that GBA = 2 AEG . ( Hint: external angles.) inally, show that GBC = AEG , and use this to show that ABC = 3 GBC . How do we use this to trisect an angle? Given an angle, draw it as ABC where AC is perpendicular to BC . Now using B in place of ) and the line AC in place of L , with a = 2 AB , carry out the construction of the conchoid. Show that E is the intersection of the line through A parallel to BC with the conchoid. But then we have constructed the angle GBA to be one-third of the given angle. Challenge problems:...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08