Construct a segment whose measure is [math]\frac14[/math] the length of [math]\overline{PQ}[/math]. [i]Note[/i]: Drag points [i]P[/i] and [i]Q[/i] to try different line segments.
[list=1] [*]Copy the segment and label it [math]\overline{PQ}[/math]. [*]Make a large arc intersecting [math]\overline{PQ}[/math]. [*]Make a second large arc. [*]Connect the points of intersection of the arcs. [math]\overline{PM}[/math] is congruent to [math]\overline{MQ}[/math]. [math]\overline{PM}[/math] and [math]\overline{MQ}[/math] are both [math]\frac12[/math] the length of [math]\overline{PQ}[/math]. [*]Find the midpoint of [math]\overline{PM}[/math]. [*]Make a second large arc. [*]Connect the points of intersection of the arcs. Do not erase any of your markings. [math]\overline{PN}[/math] is congruent to [math]\overline{NM}[/math]. [math]\overline{PN}[/math] is [math]\frac14[/math] the length of [math]\overline{PQ}[/math]. [/list] This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on their resources.