Topics / Non-Verbal Reasoning
Non-verbal reasoning: symmetry
Symmetry questions ask for lines of symmetry, completing a symmetric shape or spotting one that is not symmetric. A line of symmetry splits a shape into two mirror halves.
What is tested
- Counting lines of symmetry
- Completing a symmetric pattern
- Rotational symmetry
Worked example
How many lines of symmetry does a square have?
- Two through opposite sides' midpoints.
- Two through opposite corners.
- 4 in total.
Answer: 4
Exam-day checklist
- Imagine folding along the line: do the halves match?
- Check horizontal, vertical and diagonal lines.
- For completion, reflect each part across the line.
- Count each line once.
Common mistakes
- Missing diagonal lines.
- Counting a line twice.
- Assuming any even shape is symmetric.
Try it yourself
1. How many lines of symmetry does this equilateral triangle have?
Show answer
3
One from each corner to the middle of the opposite side.
2. How many lines of symmetry does this rectangle (not a square) have?
Show answer
2
One vertical and one horizontal; the diagonals do not work.
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