CPM Homework Help : CCG Problem 7-124

Carolina compared her proof to Penn’s work in problem 7-113. Like him, she wanted to prove that if $\overline{AD}//\overline{EH}$ and $\overline{BF}//\overline{CG}$ , then $a=d$ . Unfortunately, her statements were in a different order. Examine her proof below and help her decide if her statements are in a logical order in order to prove that $a=d$ .

Statements	Reasons
$\overline{AD}//\overline{EH}$ and $\overline{BF}//\overline{CG}$	Given
$a=b$	If lines are parallel, alternate interior angles are equal.
$a=c$	Substitution
$b=c$	If lines are parallel, corresponding angles are equal.
$c=d$	Vertical angles are equal.
$a=d$	Substitution

Two increasing lines, B F, & C G, cross two horizontal lines, A D, & E H, angles are labeled at intersections as follows: top left intersection, right bottom angle, a, bottom left intersection, left top angle, b, bottom right intersection, left top angle, c, right bottom angle, d.

Hint:

Is it possible to know that $a=c$ in the 3rd statement? What step is out of order?