CPM Homework Help : INT2 Problem 7-49

Carolina compares her proof to Penn’s work in problem 7-39. Like him, she wants to prove that if $\overline{AD} // \overline{EH}$ and $\overline{BF} // \overline{CG}$ , then $a = d$ . Unfortunately, her statements are in a different order. Examine her proof below and help her decide if her statements are in a logical sequence to prove that $a = d$ .

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

Be sure to start with the "Given" statements. Then, if lines are parallel, which pairs of angles will be congruent?