Construction Test Part 2: Straightedge and Compass Section

Note: There were several versions of these questions with the figures rotated. However the angles and ratios were actually all the same.

Problem 5: Composition of rotations

In this figure, let S be the rotation with center A that rotates ray e to ray f.  Let T be the rotation with center B that rotates ray g to ray h.

Construct with straightedge and compass the center of the rotation ST.

Problem 6: Dividing a segment

With straightedge and compass, divide segment MN by a point P so that

MP/PN = sqrt(2).