One way to prove that angle ABC is greater than angle D is by using the fact that the angles in a triangle add up to 180 degrees. Here are the steps:
1. Draw a line segment from A to CD so that it is perpendicular to CD. Let's call the point where the line segment intersects CD point E.
2. Since AE is perpendicular to CD, we know that angle AEC is a right angle.
3. Since ABCD is a trapezoid, we know that angle ABD is congruent to angle BCA (since they are alternate interior angles).
4. Therefore, angle ABD + angle AEC = angle BCA + angle AEC.
5. Since angle AEC is a right angle, we know that angle ABD + 90 degrees = angle BCA + 90 degrees.
6. Simplifying this equation, we get angle ABD = angle BCA.
7. Since angle ABD is greater than angle D (since it is an exterior angle of triangle BCD), we know that angle BCA is also greater than angle D.
8. Therefore, angle ABC (which is equal to angle BCA) is greater than angle D.