Symmetry
53. The Circle's Infinite Mirrors · Every line through the centre is a line of symmetry
Any line through the centre of a circle is a line of symmetry.
A circle has infinitely many lines of symmetry — every line through the centre divides it into two mirror-image semicircles. Drag the line to rotate it; the symmetry holds for any orientation.
What this lesson covers
Try to break it
Try dragging D to a different position. Does the line stop passing through O? No matter where you place D, the line always goes through O — that's because any line through the centre is a diameter. That's symmetry!
How you build it
Draw a diameter of a circle.
- Mark the centre point O.
- With centre O, draw the circle.
- Draw a line passing through O.
The proof, step by step
Prove that every line through the centre is a line of symmetry of the circle.
- A line of symmetry divides a shape into two identical halves that match perfectly when folded along the line.
- Any line passing through the centre of a circle is a diameter.
- When you fold a circle along any diameter, the two semicircles overlap exactly.
- Since this works for every possible angle, a circle has an infinite number of lines of symmetry.
Worked example
How many lines of symmetry does a circle possess?
A circle has an infinite number of lines of symmetry because any straight line passing through its centre divides it into two identical halves.
- Zero
- One
- Four
- Infinite — correct