Geometric Transformations of a Triangle

Given triangle ABC, Move the points A, etc to vary the triangle. Note the coordinates of the image vertices A' , etc. and the coordinates of the corresponding original Pts A, etc.
Are the triangles congruent? How do you know? Move slider δ to 90°, then 180`. How is this different to a translation? Compare the coordinates of ABC to those of A'B'C'. Change the angle of rotation; predict the coordinates of the new triangle. Reflect the triangle across the x and y axes; compare the coordinates to those of the original. Reflection: Compare and contrast translations, rotations and reflections. How does the resulting shape compare to the original? Will this always be true?