Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
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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