Newtonians solutions

September 12th, 2007

1. 78°

2. 25 5/7°

3. 5

4. Since AF / AB = AE / AD = 1/2 and angle FAE = angle BAD, we have triangle ABD ~ triangle AFE.  Thus, angle AEF = angle ADB, so EF ‖ BD.  Similarly, AC ‖ FG.  Since EFGH is a rectangle, we have EF is perpendicular to FG.  Since AC ‖ FG we find AC is perpendicular to EF, and since BD ‖ EF we find BD is perpendicular to AC, so ABCD is orthodiagonal.