A line of symmetry divides a plane figure into two identical, congruent halves that fit perfectly when folded. A regular polygon has all sides and all interior angles equal, giving it exactly as many lines of symmetry as it has sides. For example, an equilateral triangle has 3 lines of symmetry passing from each vertex to the midpoint of the opposite side. Conversely, a parallelogram that is not a rectangle or a rhombus lacks line symmetry because folding across any axis does not map its sides onto each other. Refer to Figure 1 for examples of an equilateral triangle and a general parallelogram.
- A line of symmetry splits a geometric figure into two congruent halves that overlap perfectly upon folding.
- Regular polygons have equal side lengths and equal interior angles, producing symmetry lines equal to side count.
- An equilateral triangle possesses 3 lines of symmetry bisecting each vertex angle and opposite side.
- A parallelogram that is not a rectangle or a rhombus has opposite sides parallel but no line of symmetry dividing it into mirror halves.
Check question: How many lines of symmetry do a regular hexagon and a parallelogram (that is neither a rectangle nor a rhombus) have, respectively?
- 6 and 0
- 6 and 2
- 3 and 0
- 6 and 4
Show answer
6 and 0. A regular hexagon is a 6-sided regular polygon, so it has exactly 6 lines of symmetry. A parallelogram that is not a rectangle or a rhombus has no line across which it folds perfectly onto itself, meaning it has 0 lines of symmetry.
