Exploring Perpendicular Bisectors: Part 1

In the app below,[br][br][list=1][*]Use the SEGMENT tool [icon]/images/ggb/toolbar/mode_segment.png[/icon]to construct a segment with endpoints [i]A[/i] and [i]B[/i]. [/*][*]Use the MIDPOINT tool [icon]/images/ggb/toolbar/mode_mirroratpoint.png[/icon] to construct the [b]midpoint[/b] of this segment. It should be named [i]C[/i]. [/*][*]Use the PERPENDICULAR LINE [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon] tool to construct a line perpendicular to segment [math]\overline{AB}[/math] that passes through the segment's midpoint [i]C[/i]. [/*][/list]
This line you've just constructed is said to be the PERPENDICULAR BISECTOR of the segment AC. Keep going: More directions appear below.
4. Use the POINT ON OBJECT [icon]/images/ggb/toolbar/mode_pointonobject.png[/icon] tool to plot a point [i]D[/i] on the perpendicular bisector. [br]5. Now construct segments [math]\overline{AD}[/math] and [math]\overline{BD}[/math]. [br]6. Now select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool. Then select (highlight) segment [br][math]\overline{AD}[/math] . Select the style bar icon (circle + triangle symbol in the upper right corner). Where it says "[b]Aa"[/b], select [b]Value[/b]. This will show its length. '[br][br]7. Repeat step (6), yet this time for segment [br][math]\overline{BD}[/math].
Now drag point [i]D[/i] all along the perpendicular bisector of segment [math]\overline{AB}[/math]. What do you notice? Be specific!
Use the ANGLE TOOL [icon]/images/ggb/toolbar/mode_angle.png[/icon] to display [math]m\angle BCD[/math]. What is it? Why does it measure what it does?
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Information: Exploring Perpendicular Bisectors: Part 1