In the GeoGebra applet below,[br][br]1) Select the CIRCLE WITH CENTER THROUGH POINT [icon]/images/ggb/toolbar/mode_circle2.png[/icon] tool. [br] Use this tool to plot a circle with center [i]A[/i] that passes through [i]B[/i]. [br][br]2) Keep this same tool selected. Now this time, construct a circle with center [i]B[/i] that passes through [i]A[/i].[br][br]3) Use the INTERSECT [icon]/images/ggb/toolbar/mode_intersect.png[/icon] tool to plot the point(s) at which these 2 circles intersect. [br] One of these points should be labeled [i]C[/i]. [br][br]4) Use the POLYGON tool [icon]/images/ggb/toolbar/mode_polygon.png[/icon] to construct the triangle with vertices [i]A[/i], [i]B[/i], and [i]C[/i]. [br]5) Now select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool. Move point(s) [i]A[/i] and/or [i]B[/i] around.
How would you classify triangle [i]ABC[/i] by its sides? Why is this?
Triangle [i]ABC[/i] is equilateral. Both circles are congruent because they have equal radii (since [math]\overline{AB}[/math] is a radius for both circles). Plus, the radius of a circle is constant. Thus, [math]AB=AC=BC[/math], which means the triangle constructed is equilateral.
[color=#0000ff]When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet. [/color]