Saccheri Quadrilateral

Girolamo Saccheri (1677-1733) was an Italian mathematician who for many years tried to prove the fifth Euclidean axiom from the other four. He based his proof attempts on the idea of negation. If he assumed Euclid 1-4 as axioms and assumed the opposite of Euclid 5 and then reach a contradiction to something known to be true, then the opposite of Euclid 5 could not hold simultaneously with the first 4 axioms, and thus Euclid 5 must be true as a consequence of the other four axioms.

One of his proof attempts involved the construction of a quadrilateral ABCD in which the sides AD and BC are assumed equal and there are right angles at points A and B. To construct this figure:

Construct segment AB
Construct perpendiculars to segment AB at the endpoints A and B.
Attach a point C to one of the perpendiculars. (To attach a point, just create the point on top of the line)
Construct a segment from point B to point C. Note that this segment will lie on top of the perpendicular below it.
Select point A and then the segment BC (you may have to click on the segment twice to select just the segment) Then click on the circle construction tool in the Construction section of the Tool Panel. This will create a circle at A of radius BC.
Find the intersection of the circle and the perpendicular at A. Call this point D.
Attach D to C.

The Saccheri Quadrilateral has some interesting properties. One of these is shown. If we measure the two upper angles, these appear to be always congruent, but never 90 degrees! Can you prove this?