Symmetry Patterns

Symmetry is one of the more abstract pattern categories in UCAT AR. While most candidates intuitively understand that a butterfly has symmetry, applying symmetry concepts under time pressure to collections of abstract shapes requires deliberate practice. This lesson covers both line symmetry (reflective) and rotational symmetry, and shows how each appears in AR questions.

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Two Types of Symmetry

Line Symmetry (Reflective Symmetry)

A shape or arrangement has line symmetry if you can draw a line through it such that one side is a mirror image of the other. This line is called the axis of symmetry or line of symmetry.

Shape	Lines of symmetry
Circle	Infinite
Square	4 (two diagonals, one horizontal, one vertical)
Rectangle	2 (one horizontal, one vertical)
Equilateral triangle	3
Isosceles triangle	1
Scalene triangle	0
Regular pentagon	5
Regular hexagon	6
Parallelogram	0
Arrow (symmetric)	1 (along its length)

Rotational Symmetry