Check out the attached image for the answers all on one sheet.
------------------------------------------------------------------------------
Label each row 1, 2, ..., all the way up to row 7. I'll refer to each statement and reason by the row number. For example, in row 2 we have "statement 2" and "reason 2". Statement 2 is already filled in for us while Reason 2 is blank.
Statement 1 has "CD perpendicular to AE". This is given to us to be true as shown in the "given" portion at the very top of the problem (just under the diagram).
What's also given to us is the fact that "line segment CD is parallel to line segment GH". So we'll write "given" for reason 2.
------------------------------------------------------------------------------
Next up is reason 3, which is "definition of perpendicular". Why is this? Because the statement "angle ABD is a right angle" means angle ABD is 90 degrees. The term "perpendicular" means two lines or line segments or rays cross/meet at a 90 degree angle.
Now onto reason 5. Note how angle ABD and angle GEF are alternate exterior angles. They are outside of the train tracks (CD and GH) and lay on alternate sides of the line FA. Since CD is parallel to GH (see line 2), this means the alternate exterior angles are congruent. For reason 5, we'll put "alternate exterior angles theorem"
------------------------------------------------------------------------------
Statement 7 is the the thing we want to prove. For any proof, the last statement is ALWAYS what you want to prove. If there's anything after this statement then we still have work to do and the proof isn't done. This is the last stop so to speak. So we simply write exactly what we want to prove (next to the "prove:" portion just below the diagram)
Reason 7 is "definition of perpendicular" because GEF is a right angle so GH is perpendicular to line FA. Like with reason 3, a 90 degree angle forms.
------------------------------------------------------------------------------
Once again, check out the attached image to see all of the answers in the right spots.
