In quadrilateral abcd, assume that angle a = 90 degrees = angle c. draw diagonals ac and bd and show that angle dac = angle dbc.

The drawing must be a square for this to be true. After you draw the diagonals, explain that since it is a square, all sides are congruent so since the legs are congruent in the two triangles formed, by Isosceles Triangle Theorem, DAC and DBC are both 45 degrees, showing us that angle DAC = Angle DBC.