G.CO.D.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Example Problems
There is exactly one reflection and no rotation that sends the convex quadrilateral onto itself. What shape(s) could quadrilateral be? Explain.
Suppose is a quadrilateral for which there is exactly one rotation, through an angle larger than and less than , which maps it to itself. Further, no reflections map to itself. What shape is ?
Choose two distinct points and in the plane.

a. For which points
is a right triangle?

b. For which points
is an obtuse triangle (that is, a triangle with one obtuse angle)?

c. For which points
is an acute triangle (that is, a triangle with three acute angles)?

Justify your responses.
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