Let ABCDEFGHIJKL be a regular 12-sided polygon. TRUE or FALSE: The diagonals AE, CF, and DH intersect in a point.

Each of the 12 angles is 10*180º/12= 150º

Call the possible point of crossing M

Consider triangles DEM and FEM.  If M really is a point then EM will be the same length in each.

Angles MED and MDE are both 45º so DEM is 90º.  So EM is √2/2 times the side length.

Angle FME is 30º and MEF is 105º so FEM is 45º.  Using the law of sines, EM is √2/2 times the side length.

So the answer is TRUE

Posted by Jer on 2013-08-23 20:17:56