The mission was to prove that a=d if AD∥ EH and BF∥ CG. Let's show the original proof from the mentioned exercise.
Statement
Reason
1.
AD∥ EH and BF∥ CG
1.
Given
2.
a=b
2.
Alternate Interior Angles Theorem
3.
b=c
3.
Corresponding Angles Theorem
4.
a=c
4.
Transitive Property of Equality
5.
c=d
5.
Vertical Angles Theorem
6.
a=d
6.
Transitive Property of Equality
If we can change the order in which the proof was written, it would mean that those parts that are changed were independent of other parts of the proof. The only part of the proof that hinges on what comes before it are the lines where we use the Transitive Property of Equality. Therefore, we can change the proof in the following way.
