Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
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 ?
A cheerleading coach maps out formation on the gym floor. To get formation , the squad slides to the left without turning or flipping. The two formations have the same shape and face the same way.
What single transformation was applied to formation to get formation ?
What single transformation was applied to formation to get formation ?
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