Given the following: [math]\overline{AC} \cong \overline{BD}[/math] [math]\overline{AB} \perp \overline{AC}[/math] [math]\overline{AB} \perp \overline{BD}[/math] [math]\overline{WY} < \overline{XZ}[/math] [math]\overline{WX} \perp \overline{WY}[/math] [math]\overline{WX} \perp \overline{XZ}[/math] Are [math]\overline{AB}[/math] and [math]\overline{CD}[/math] parallel? Are [math]\overline{WX}[/math] and [math]\overline{YZ}[/math] parallel?
[list=1] [*][math]\overline{AC}[/math] and [math]\overline{BD}[/math] intersect [math]\overline{AB}[/math] at the same angle and [math]\overline{AC} \cong \overline{BD}[/math]. [math]\overleftrightarrow{AB}[/math] will never cross [math]\overleftrightarrow{CD}[/math]. Therefore, [math]\overline{AB}[/math] is parallel to [math]\overline{CD}[/math]. [*][math]\overline{WY}[/math] and [math]\overline{XZ}[/math] intersect [math]\overline{WX}[/math] at the same angle, but [math]\overline{WY} < \overline{XZ}[/math]. As you move from [math]Z[/math] to [math]Y[/math] on [math]\overleftrightarrow{YZ}[/math], you move closer to, and will eventually intersect [math]\overleftrightarrow{WX}[/math]. Therefore, [math]\overline{WX}[/math] is not parallel to [math]\overline{YZ}[/math]. [/list] This applet is provided by Walch Education as supplemental material for the [i]UCSS Secondary Math I[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.