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.

Mitsubishi Logo

Rotation: L & H

Rotation: Quadrilateral

The distances of the reflected shape and the original shape remain the same from point to point.

No matter where are vertex is, the angles of both shapes are still equal.

When animated, the distances between AD and A'D remain the same.

All the distances in pairs (eg AD and A'D) are all the same.

Angles are invariant under a reflection.
The lengths of the sides of an object are invariant under a reflection.
Points on the mirror line are invariant under a reflection.


I have found that all angles and all distances and measurements were invariant between original shapes and reflected shapes everything was the same except that the shape was reversed.

Reflection: F, Tree, and Shape.

Reflection: Triangle

The labeling system shows that when you mirror the object the labeled points are reversed.

When the mirror line passes through the base of the original triangle, the mirrored triangle is partially inside the original one

When a point of the original object is on the mirror line, it is called an invariant point.