Symmetry
110. Spin & Stay the Same · Rotation preserves shape and size
Rotating a figure never changes its side lengths or angles.
A rotation turns a figure about a fixed point (the centre of rotation) by a fixed angle. Rotation preserves all distances and angles — the rotated figure is congruent to the original.
What this lesson covers
Try to break it
Drag B and C to reshape the triangle. Drag R to rotate it! Notice how every side and angle stays identical to the original.
The proof, step by step
Prove that rotation keeps every side length and angle unchanged.
- Rotation moves every point around a fixed centre.
- The distance from the centre to each point remains constant.
- Therefore, all side lengths and angles are preserved.
Worked example
A triangle PQR is rotated 60° about vertex P to form triangle P'Q'R'. Which of the following statements is always true?
Rotation is a rigid transformation. It preserves distances from the centre and all side lengths and angles. Only orientation changes.
- The triangle changes its size but not its shape.
- The distance from the centre of rotation to each vertex remains the same. — correct
- The orientation of the triangle remains exactly the same.
- The sum of angles changes by 60°.