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# Class Note for MATH 409 with Professor Martin at KU

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COURSE
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KARMA
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This 1 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 24 views.

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Date Created: 02/06/15
Suppose that AABC AA B C and that you can t get one triangle from the other by fewer than two re ections How can you tell whether two or three re ections are required The answer actually doesn7t have to do with whether the triangles are themselves symmetric eigi equilateral or isosceles Rather what matters is the clockwise order of the vertices is it ABC which is the same thing as BCA or CBA or ACB which is the same thing as BAC or CAB Any re ection will reverse this clockwise orderi Therefore a composition of an even number of re ections will keep this order the same while a composition of an odd number of re ections will reverse it Now it true that if T and T are equilateral or isosceles triangles and T E Tquot then there exists a line Z such that TAT T3 That is you can get from T to T by a single re ectioni However 7 this is a subtle point 7 you can t control which vertex goes to which one For example if T AABC and T AABC are the following pair of congruent triangles then by the clockwiseness agument above there can be no re ection m such that 7 A A 7 B Bquot and TAG C5 There does however exist a re ection Tm shown such that 7 A Aquot 7 B Cquot and TAG B3 B 0 On the other hand two congruent triangles don7t need to be isosceles or equilateral in order for one to be transformable to the other by a single re ectioni After all you can take any old scalene triangle T and any old line Z and de ne T TAT then T and T are congruent scalene triangles related by one re ectioni

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