Fast!
true or false? based on the only given information it is guaranteed that ab is perpendicular to cd.
given:
ad is congruent to bd
ac is congruent to bc
cd is congruent to cd

Yes, It forms two right angle triangles (which are the same) because AD is the same length to DB and AC is the same length to BC. right angle triangles meet a line at 90° and thus CD must be perpendicular to AB.

Hope this helps.