How to determine point is Inside the Triangle?

An Isosceles Right Triangle has _____________ (Line, Point or Both) Symmetry.?

• I know that A right triangle has line symmetry, but does It have Point Symmetry? The Def. of Point Symmetry is Point of rotation (according to The Teacher). Point of Rotation: A figure in a plane has rotational symmetry if the figure can be mapped onto itself by a rotation of 180 degrees or less. Rotation: A type of transformation in which a figure is turned around a fixed point, called the center of rotation. Using these definitions, I know that if you rotate the triangle less than 360 degrees, you don't have symmetry (the figure is not mapped onto itself). Can you however rotate the figure 0 degrees, in which the figure is mapped onto itself? I believe that this follows the defs., and I realize that this gives every figure a point of symmetry (But couldn't this just be a type of reflexive property?). Is there a theorem somewhere that says that a rotation must be greater that 0?

• Answer:

  A rotation of 0 degrees doesn't move or transform the figure at all. It's like sliding it by a vector of <0, 0>, or enlarging it by a scale factor of 1. No movement = no transformation. Your isosceles right triangle will have line symmetry, only.