Help with Algebra 2 problem

The correct answer is (D)

If this is true, angle ADC, by assumption,  =  90°....so ADB also = 90°

Thus, AD will be perpendicular to lines extended through BD and CD

And by Euclid - Book XI - Proposition IV :

"If a straight line is set up at right angles to two straight lines which cut one another at their common point of section, then it is also at right angles to the plane passing through them."

Here's the full proof of this : http://aleph0.clarku.edu/~djoyce/java/elements/bookXI/propXI4.html