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Michael Lambrou

Posts: 70
Registered: 12/3/04
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Posted: Dec 2, 2004 9:43 AM
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"Edwin McCravy" &lt;AnlytcPhil@aol.com&gt; wrote in message <a href="news://tnhtu2svcraf@legacy...">news://tnhtu2svcraf@legacy...</a>
&gt; Given:
&gt;
&gt; (1) Triangles ABC and XYZ are not congruent under any rotation. Angle
&gt; C has the same measure as angle Z.
&gt;
&gt; (2) There exists a real number t such that
&gt;
&gt; |AC|^t + |BC|^t = |AB|^t and
&gt; |XZ|^t + |YZ|^t - |XZ|^t
&gt;
&gt; Prove triangles ABC and XYZ are right triangles, i.e., that t=2 and
&gt; the angles C and Z are right angles.
&gt;


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.



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