You can also use the COMPASS tool to construct an EQUILATERAL TRIANGLE. Here's how:[br][br]1) Use the SEGMENT [icon]/images/ggb/toolbar/mode_segment.png[/icon] tool to construct a segment with endpoints [i]A[/i] and [i]B[/i]. [br]2) Select the COMPASS [icon]/images/ggb/toolbar/mode_compasses.png[/icon] tool. Then select point [i]A[/i], then select point [i]B[/i]. [br] (You should notice another circle appear. This circle has a radius = [i]AB[/i]). [br] Click on point [i]A[/i]. [br][br]3) Select the COMPASS tool again. This time, simply click on the segment [math]\overline{AB}[/math] itself. [br] Then click on point [i]B[/i]. [br][br]4) Use the INTERSECT [icon]/images/ggb/toolbar/mode_intersect.png[/icon] tool to plot the point(s) of intersection of the two circles you've just[br] constructed in steps (2) & (3). [br][br]5) Use the POLYGON [icon]/images/ggb/toolbar/mode_polygon.png[/icon] tool to construct the triangle formed by [i]A[/i], [i]B[/i], & the point you constructed in [br] step (4).
Why is this triangle equilateral?[br]
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=BC=AC[/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]