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Rotational Symmetry

Rotational Symmetry problems present figures that have rotational symmetry of order n (2, 3, 4, 5, 6, or 8). You must identify the missing element such that when the figure is rotated by 360°/n degrees, it looks identical. Common examples include pinwheels, windmills, stars, and rosettes.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Rotational Symmetry

Rotational Symmetry problems present figures that have rotational symmetry of order n (2, 3, 4, 5, 6, or 8). You must identify the missing element such that when the figure is rotated by 360°/n degrees, it looks identical. Common examples include pinwheels, windmills, stars, and rosettes.

Prerequisites

Understanding of rotational symmetry Concept of order of rotational symmetry (n-fold symmetry) Angular measurements (90°, 120°, 180°, 60°, 45°) Basic shape recognition
Why This Matters: Rotational Symmetry problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test understanding of rotational symmetry and angular patterns.

How to Solve Rotational Symmetry Problems

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Step 1: Identify the order of rotational symmetry (n = 2, 3, 4, 5, 6, or 8)

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Step 2: Determine the rotation angle = 360°/n

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Step 3: Observe the pattern in the completed positions

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Step 4: The missing position must be the rotation of an existing position by the rotation angle

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Step 5: Apply the rotation to the corresponding existing element to find the missing element

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Step 6: Verify that all positions satisfy rotational symmetry

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Step 7: Select the correct answer option

Pro Strategy: Identify the rotation angle from the pattern. The element at the missing position is the rotation of the element at the corresponding position by the rotation angle (or multiples thereof).

Example Problem

Example: A 4-pointed star has points at top, left, and right. The bottom point is missing. What completes the pattern? Solution: Step 1: Order of symmetry = 4 (90° rotation) Step 2: Rotation angle = 90° Step 3: Top point (0°) rotates to left point (90°), left to bottom (180°), bottom to right (270°) Step 4: Bottom point should be the same as top point (since top rotates to bottom after 180°) Answer: Bottom point identical to top point

Pro Tips & Tricks

  • 90° rotational symmetry (4-fold): positions at 0°, 90°, 180°, 270° are identical
  • 120° rotational symmetry (3-fold): positions at 0°, 120°, 240° are identical
  • 180° rotational symmetry (2-fold): opposite positions are identical
  • 60° rotational symmetry (6-fold): positions at 0°, 60°, 120°, 180°, 240°, 300° are identical
  • 45° rotational symmetry (8-fold): positions at 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315° are identical
  • For n-fold symmetry, the figure looks the same after rotation by 360°/n

Shortcut Methods to Solve Faster

For 90° symmetry, all four arms are identical
For 180° symmetry, opposite arms are identical
For 120° symmetry, every third arm is identical
If the missing position is opposite an existing position, use 180° rotation
If the missing position is 90° from an existing position, use 90° rotation

Common Mistakes to Avoid

Using the wrong rotation angle for the symmetry order
Forgetting that the element itself may rotate (e.g., an arrow points in the direction of rotation)
Not identifying the correct center of rotation
Assuming all points are identical when they may rotate orientation

Exam Importance

Rotational Symmetry is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
INSURANCE
1-2 questions

Ready to Master Rotational Symmetry?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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