CPM Homework Help : CCG Problem 8-22

Suzette started to set up a proof to show that if $\overline { B C } / / \overline { E F }$ , $\overline { A B } / / \overline { D E }$ and $AF = DC$ , then $\overline { B C } \cong \overline { E F }$ . Examine her work below. Then complete her missing statements and reasons.

2 triangles, share a part of their horizontal sides, horizontal top side, F D, of triangle, F E D, extends to the right, horizontal bottom side, A C, of triangle, A B C, extends to the left.

Statements	Reasons
$\overline { B C } / / \overline { E F }$ , $\overline { A B } / / \overline { D E }$ and $AF = DC$
$m\angle BCF = m\angle EFC$ and $m\angle EDF = m\angle CAB$
	Reflexive Property
$AF + FC = FC + DC$	Additive Property of Equality (adding the same amount to both sides of an equation keeps the equation true)
$AC = DF$	Segment addition
$\Delta ABC \cong \Delta DEF$
	$\cong\Delta\text{s}\rightarrow\;\cong\text{ parts}$

Answer:

Statements	Reasons
$\overline{BC} // \overline{EF}, \overline{AB}// \overline{DE}$ , and $AF = DC$	Given
$m\angle BCG = m\angle EFC$ and $m\angle EDF = m\angle CAB$	If two lines cut by a transversal are parallel, then alternate interior angles are equal.
$\boldsymbol{FC=FC}$	Reflexive Property
$AF + FC = FC + DC$	Additive Property of Equality (adding the same amount to both sides of an equation keeps the equation true)
$AC = DF$	Segment addition
$\Delta ABC \cong \Delta DEF$	$\textbf{ASA}\mathbf{\cong}$
$\boldsymbol{\overline{BC} \cong \overline{EF}}$	$\cong \Delta\text{s} \rightarrow \; \cong$ parts