Sheet 13 of 14 路 Non-verbal Reasoning
Rotation, reflection and symmetry
Turning, flipping and folding shapes in non-verbal reasoning. 10 rules, each with a worked example.
Turning (rotation)
Quarter and half turns
90掳 = a quarter turn 路 180掳 = a half turn 路 360掳 = back to the start
ExampleAn arrow pointing up, turned 180掳, points downClockwise and anticlockwise
90掳 anticlockwise equals 270掳 clockwise
ExampleAn arrow pointing right, turned 90掳 anticlockwise, points upTrack one feature
Follow one stand-out part (a dot, a corner, a short line) as the shape turns
ExampleA dot in the top-left corner, turned 90掳 clockwise, ends up top-rightTip: Turning never changes the size, shading or number of parts.
Flipping (reflection)
Mirror lines
Each point ends up the same distance from the mirror line, on the other side
Upright or flat mirror
Upright mirror line: left and right swap 路 Flat mirror line: top and bottom swap
ExampleA dot top-left: in an upright mirror it goes top-right; in a flat mirror, bottom-leftRotation or reflection?
If no turn makes one shape into the other, it has been reflected
ExampleL and a back-to-front L: no turn swaps them, so one is a reflectionTip: Reflections look like mirror writing.
Slanted mirror lines
Turn the page until the mirror line is upright, then reflect as normal
Symmetry
Lines of symmetry
Fold along the line: the two halves match exactly
ExampleRectangle 2 路 equilateral triangle 3 路 square 4 路 circle: endlessRotational symmetry
Order equals how many times it looks the same in one full turn
ExampleRectangle: order 2 路 equilateral triangle: order 3 路 square: order 4Complete the picture
On a grid, count the squares out from the mirror line and copy them on the other side
Want the full explanation?
The study guide goes through each rule step by step, with more examples.