Consider a paper parallelogram ABCD with AB parallel to CD, AC parallel to BD and ∠ABC = 54^o. It is known that |AB| > |AC|.

Vertex B is folded on to vertex D forming the crease EF with E in AB and F in CD such that |EF|= |CD|

Determine the ratio |AB|:|AC|

Constructing this in Geometers' Sketchpad, it seems that AB doesn't exceed AC unless E is on an extension of AB beyond the edge of the paper, rather than on segment AB itself.

Posted by Charlie on 2014-12-19 10:49:33