CPM Homework Help : CCG Problem 7-113

Penn started the proof below to show that if $\overline{AD}//\overline{EH}$ and $\overline{BF}//\overline{CG}$ , then $a=d$ . Unfortunately, he did not provide reasons for his proof. Copy his proof and provide a justification for each statement.

Hint:

For each numbered statement, write how you know it to be true. Think about how angles and parallel lines relate to each other.

Statements	Reasons
$\overline{AD}//\overline{EH}$ and $\overline{BF}//\overline{CG}$	Justification for Statement 1: Given information.
$a=b$	Justification for Statement 2: When lines are parallel, then the alternate interior angles are congruent.
$b=c$
$a=c$
$c=d$
$a=d$

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.