You can 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 the triangle you constructed 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. [/color]
Use the straightedge and compass tools to construct a square in the window below. Show all arc marks and darken your final answer.
Use the straightedge and compass tools to construct something else in window below. Show all arc marks and darken your final answer.
What did you construct above? Explain your strategy.