Symmetry Kit for School Maths Lab

Quick Answer: A Symmetry Kit is a set of maths lab materials for exploring line (mirror) symmetry and rotational symmetry in shapes and patterns. Students use the symmetry kit to find lines of symmetry in polygons, complete half-drawn figures and work out the order of rotational symmetry.

Two Kinds of Symmetry in One Kit

A figure has line symmetry when a mirror placed along a line reproduces the missing half exactly, and rotational symmetry when it fits onto itself after a turn of less than a full rotation. Kits for this topic are built to let students test both ideas physically rather than by eye, typically with safety mirrors, shape pieces and pattern cards, although contents vary between suppliers and should be confirmed.

With a mirror, students stand it on a candidate line of a shape and check whether the reflection completes the figure. A rectangle passes along its two midlines but fails along its diagonals, a result many pupils do not predict. Regular polygons make a good investigation: an equilateral triangle has 3 lines, a square 4 and a regular hexagon 6, which leads to the rule that a regular n-sided polygon has n lines.

Rotational symmetry is found by tracing a shape, turning the tracing about its centre and counting how many times it matches in one full turn. A square matches 4 times, so its order of rotational symmetry is 4; a parallelogram matches twice but has no line of symmetry at all, which makes it a useful case for discussion.

Applications

• Testing which polygons have which lines of symmetry and recording the results in a table
• Completing a half-drawn figure or pattern on squared paper across a mirror line
• Finding the order of rotational symmetry by turning traced shapes
• Looking for symmetry in letters, logos, rangoli designs and flags

Care & Handling

• Handle mirror pieces by the edges and keep fingerprints off the reflecting face; wipe with a soft dry cloth.
• Check mirror edges for chips or cracks before handing them out, and withdraw any damaged piece.
• Store mirrors in their slots, or face to face with a sheet of paper between them, to prevent scratches.
• Count shape pieces and cards back into the symmetry kit box so investigations can be repeated.

Specifications

Why Choose LabEquip

Middle school geometry teachers use a kit like this for group investigations in which each table tests shapes and reports back. The kit sits in LabEquip’s Mathematics School Lab Products range beside the Plastic Tangram, whose pieces also make good symmetry puzzles. Ask for current contents through the contact page.

Frequently Asked Questions

How do line symmetry and rotational symmetry differ?

Line symmetry means one half of a figure is the mirror image of the other half across a line. Rotational symmetry means the figure looks the same after being turned about its centre through less than a full turn. A figure can have one type, both types or neither.

Does a rectangle have four lines of symmetry?

No. A rectangle that is not a square has only two lines of symmetry, through the midpoints of opposite sides. Mirroring along a diagonal does not match the corners, which students can check quickly with a mirror.

How is the order of rotational symmetry found?

Trace the shape, place the tracing on the shape and turn it about the centre. Count how many times it fits exactly during one complete turn, including the starting position. That number is the order. A shape that fits only once has order 1, meaning no rotational symmetry.

How many lines of symmetry does a regular polygon have?

A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n. A regular pentagon therefore has 5 lines and order 5. When the number of sides is odd, each line runs from a vertex to the midpoint of the opposite side.

Can a shape have rotational symmetry without line symmetry?

Yes. A parallelogram that is not a rectangle or a rhombus fits onto itself after a half turn but has no line of symmetry. Some pinwheel patterns behave the same way, which makes them good examples for discussion.

How should students use the mirror correctly?

Stand the mirror upright along the line being tested and look into it from the side where the shape is. If the half in front of the mirror together with its reflection looks exactly like the complete shape, the line is a line of symmetry.

Last Updated: September 2026