"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.