In Inner Product Spaces
The isosceles triangle theorem holds in inner product spaces over the real or complex numbers. In such spaces, it takes a form that says of vectors x, y, and z that if
then
Since
and
where θ is the angle between the two vectors, the conclusion of this inner product space form of the theorem is equivalent to the statement about equality of angles.
Read more about this topic: Isosceles Triangle Theorem
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