Symmetries of a Circle
A circle has reflection symmetry about every diameter and rotational symmetry about its centre for any angle of rotation.
Practice This ConceptMain explanation
Teacher explanation
If a circle is folded along any diameter, the two halves match exactly. If it is rotated around its centre, it still looks the same because all boundary points remain at the same distance from the centre.
Example
A wheel rotated by 40 degrees about its centre still has the same circular outline. A fold along any line through the centre divides the circle into two equal halves.
Simple analogy
Through the centre, perfect mirror.
Common confusion
Students sometimes think only horizontal and vertical diameters are lines of symmetry. Actually, every diameter is a line of symmetry.
Exam tip
For symmetry questions, check whether the line passes through the centre. A chord not passing through the centre is not a line of symmetry of the whole circle.
Answer writing and exam use
1-mark use
Write the exact meaning of symmetries of a circle in one clean line.
2-mark use
Define symmetries of a circle and add one example or condition.
3-mark use
Explain symmetries of a circle, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
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