Symmetry Pattern Questions: Recognising and Completing Symmetrical Figures
Symmetry pattern questions test your ability to spot and complete symmetrical figures. A figure is symmetrical when one part mirrors, rotates into, or translates to match another part. Abstract reasoning tests use symmetry in matrices, figure series and "complete the pattern" questions. This article explains the main types of symmetry and how to apply them.
Types of Symmetry
Reflective (mirror) symmetry – One half of the figure is the mirror image of the other. A vertical line down the centre creates two identical halves. Or a horizontal line. Or a diagonal. The "line of symmetry" is the axis. To complete a reflective pattern, mirror the given part across the axis.
Rotational symmetry – The figure looks the same when rotated by a certain angle (e.g. 90°, 120°, 180°). A square has 4-fold rotational symmetry (90°); an equilateral triangle has 3-fold (120°). To complete a rotational pattern, rotate the given part by the correct angle.
Translational symmetry – The same motif repeats at regular intervals, like a wallpaper pattern. The motif doesn't flip or rotate; it shifts. To complete a translational pattern, copy the motif in the direction of the shift.
Glide reflection – A combination of reflection and translation. The motif is reflected and then shifted. Less common in tests but possible.
In abstract reasoning, reflective and rotational symmetry are most common. Translational symmetry appears in repeating patterns.
How Symmetry Appears in Questions
Complete the figure – Half of a symmetrical figure is given. You choose the other half from options. Identify the axis (vertical, horizontal, diagonal) and mirror accordingly.
Find the odd one out – One figure breaks the symmetry that the others share. The odd one may have no symmetry, a different axis, or an extra element that breaks it.
Matrix completion – Rows or columns may follow symmetry. For example, the middle column is the mirror axis; left and right columns mirror each other. Or the pattern rotates 90° per row.
Series completion – The sequence may alternate between symmetrical and non-symmetrical figures, or the symmetry axis may rotate.
Step-by-Step Approach
Step 1: Identify the symmetry type – Is it reflective, rotational or translational? Look at the given part. Does it mirror, rotate or repeat?
Step 2: Find the axis or centre – For reflective symmetry: where is the line of symmetry? For rotational: where is the centre? For translational: what is the repeat distance?
Step 3: Apply the transformation – Mirror across the axis, rotate around the centre, or shift by the repeat distance. Mentally construct the missing part.
Step 4: Match the options – Which option matches your construction? Be careful: some options may be reflections across the wrong axis or rotations by the wrong angle.
Step 5: Verify – Check that the complete figure is symmetrical. Every point on one side should have a corresponding point on the other.
Common Pitfalls
Wrong axis – You assumed a vertical axis when it was horizontal or diagonal. The options may include the "wrong" reflection. Check the orientation of the given part.
Wrong rotation direction – Clockwise vs anticlockwise matters. Rotate in the direction implied by the pattern.
Ignoring the centre – In rotational symmetry, the centre of rotation is fixed. Elements farther from the centre move more. Don't assume the centre is at the geometric centre—it might be offset.
Confusing reflection with rotation – A 180° rotation can look like a reflection for some figures. But for asymmetric shapes, they differ. Trace one distinctive feature to see which transformation applies.
Partial symmetry – The figure may be symmetrical in one way but not another. For example, it has vertical symmetry but not horizontal. Focus on the symmetry that the question uses.
Tips for Speed
Fold mentally – Imagine folding the figure along the axis. The two halves should coincide. Use this to visualise the missing part.
Trace one element – Pick a distinctive element (a dot, a corner). Where would its mirror or rotated counterpart be? That helps you place the rest.
Use the options – If you're unsure of the axis, compare options. One will be the correct reflection; others will be wrong reflections or rotations. Eliminate the wrong ones.
Check diagonals – Don't forget diagonal axes. A figure can have symmetry about a 45° line.
Practice with abstract reasoning questions and the abstract reasoning test.
Frequently Asked Questions
How do I know if it's reflective or rotational symmetry?
For reflective symmetry, there's a line; one half is the mirror image. For rotational symmetry, the figure repeats when rotated. Asymmetric shapes (e.g. "L") can distinguish: a mirror gives a different shape than a 180° rotation.
Can a figure have more than one type of symmetry?
Yes. A square has 4 reflective axes and 4-fold rotational symmetry. The question will typically focus on one transformation.
What if the axis is not obvious?
Look at the given part. Its "partner" must be at an equal distance from the axis. Sometimes the axis is implied by the layout (e.g. centre of a matrix cell).