Equilateral Triangle Construction and Observation
Use the limited toolbar below to construct an equilateral triangle.
Use the DISTANCE tool 
afterwards to show that all 3 sides of your triangle have equal lengths.
Why does your method of construction even work? How can we justify why all 3 sides are equal (aside from the fact GeoGebra says so)?
Use the ANGLE 
tool to measure all 3 angles of this equilateral triangle. Then select the MOVE 
tool and drag its vertices around. What do you notice?