CPM Homework Help : INT2 Problem 7-39

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.

Statements	Reasons
$\overline{AD} // \overline{EH}$
$a = b$
$\overline{BF} // \overline{CG}$
$b = c$
$a = c$
$c = d$
$a = d$

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.

Hint:

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

Partial Answer 1:

Justification for statement 1: Given

Partial Answer 2:

Justification for statement 2: alternate interior angles are congruent