)nB GSP!KPC`B +0BCB4+0A\B4+ AE)XKv(T| Problem: Given segment AB and point C, construct, using only a Euclidean (collapsing) compass, the image, C', of C under the translation that takes A to B. Thus one needs the point C' such that AB and CC' are parallel and equal in length.
On an exam, one geometry student did this: Construct the equilateral triangle ACX (with X toward AB) and construct the equilateral triangle ABY (with Y toward C). Using X and Y construct the equilateral triangle XYH.
Comparing the slope and length of AB with that of CH leads to the conjecture that H = C', the desired point. Draging C and B seems to confirm the conjecture. How can this be proven?
Mel Thornton, University of Nebraska-LincolnlnlnW W0c7c0>LOt<!4CB4C9?5%F?5%Ft!3\B4C9?5%F?5%Fbl2\B4BP ?5%F?5%F'9;1`BBP ?5%F?5%F*P
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