📌 Key Points
- Line symmetry: Figure folds along a line so both halves match exactly.
- Line of symmetry (axis): The fold line dividing figure into identical mirror images.
- Rotational symmetry: Figure looks same after rotating less than 360° about a point.
- Order of rotational symmetry: Number of times figure matches itself in 360° rotation.
- Center of rotation: Fixed point about which figure rotates for rotational symmetry.
- Point symmetry (180° rotation): Figure looks same when rotated 180° about center.
- Square: 4 lines of symmetry, rotational order 4 (90° rotation).
- Rectangle: 2 lines of symmetry, rotational order 2 (180° rotation).
- Equilateral triangle: 3 lines of symmetry, rotational order 3 (120° rotation).
- Regular polygon with n sides: n lines of symmetry, rotational order n.
- Circle: Infinite lines of symmetry (all diameters), infinite rotational order.
- Rotational order formula: Order = 360° ÷ rotation angle.
- A figure can have line symmetry, rotational symmetry, both, or neither.
- Parallelogram: No line symmetry, but has 180° rotational symmetry (order 2).
- Scalene triangle: No line symmetry, no rotational symmetry.
📘 Important Definitions
🔢 Formulas & Laws
Order of Rotational Symmetry
Order = 360° ÷ Rotation Angle
If order = n, rotation angle = 360° ÷ n
Regular Polygon Symmetry
For n-sided regular polygon: Lines of symmetry = n, Rotational order = n
Angle of rotation = 360° ÷ n
Circle Symmetry
Lines of symmetry = ∞ (infinite), Rotational order = ∞ (infinite)
Any diameter is a line of symmetry
Rectangle Symmetry
Lines of symmetry = 2, Rotational order = 2 (180° rotation)
Lines through horizontal and vertical midpoints (not diagonals)
Square Symmetry
Lines of symmetry = 4, Rotational order = 4 (90° rotation each)
2 diagonals + 2 midlines; 360° ÷ 4 = 90°
⚠️ Common Mistakes
✗ Wrong: Thinking rectangle has 4 lines of symmetry like square (it only has 2).
✓ Correct: Rectangle has 2 lines of symmetry (horizontal and vertical midlines). Diagonals are NOT lines of symmetry.
✗ Wrong: Confusing order with rotation angle. Order 4 means 4 times matches, not 4°.
✓ Correct: Order = 360° ÷ rotation angle. Order 4 means 360° ÷ 4 = 90° rotation angle.
✗ Wrong: Thinking all shapes with line symmetry have rotational symmetry.
✓ Correct: Not all: Isosceles triangle has 1 line symmetry but no rotational symmetry. Parallelogram has no line symmetry but order 2 rotation.
✗ Wrong: Forgetting that circle has infinite symmetries (both line and rotational).
✓ Correct: Circle has infinite lines of symmetry (all diameters) and infinite rotational order.
✗ Wrong: Assuming scalene triangle has some symmetry.
✓ Correct: Scalene triangle (all sides unequal) has no line symmetry and no rotational symmetry.
📝 Exam Focus
These questions are frequently asked in CBSE exams:
🎯 Last-Minute Recall
Close your eyes and try to recall: Key definitions, formulas, and 3 common mistakes. If you can recall 80% without looking, you're exam-ready!