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.
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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