Triangle and Rotation Answers

From the triangle beside, we can see that both the original triangle and the rotated share that point which it was rotated on.

The actual shape remains the same (invariant) which means that the shape has been unaltered, merely rotated.

All the angles in comparison between the original triangle and rotated triangle were the same, there was no change in the angles post rotation. This can be proven by moving around the points of the original triangle and it's image will follow.

The lengths, like the angles, did not change upon rotation, they were also the same in comparison between the original and rotated triangles.

Angles are invariant under a rotation.
The lengths of the sides of an object are invariant under a rotation.
The centre of rotation is the only invariant point.