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[No Subject]
Posted:
Dec 2, 2004 9:43 AM



"Edwin McCravy" <AnlytcPhil@aol.com> wrote in message <a href="news://tnhtu2svcraf@legacy...">news://tnhtu2svcraf@legacy...</a> > Given: > > (1) Triangles ABC and XYZ are not congruent under any rotation. Angle > C has the same measure as angle Z. > > (2) There exists a real number t such that > > AC^t + BC^t = AB^t and > XZ^t + YZ^t  XZ^t > > Prove triangles ABC and XYZ are right triangles, i.e., that t=2 and > the angles C and Z are right angles. >
Unfortunately it is false. Take e.g ABC with sides AC = BC = 2 AB = (cube root of 16) = approx. 2.52 and t = 3. Then AC^3 + BC^3 = 16 = AB^3. For XYZ take a similar triangle with all sides multplied by a factor of 2. All conditions hold, except the conclusion.
Regards, Michael.



