How many lines of symmetry does it have?
A normal-level "Count" problem.Many people count only the corner-to-corner lines and stop at half the answer. Do not forget the edge-midpoint lines.
GivenA regular 6-sided polygon
Hints
- A line of symmetry is a line you can fold along so the two halves match. Here is one: join two opposite corners and fold — the halves match exactly.
- The same works at the other corners. With 6 corners there are 3 opposite pairs, so 3 lines of this kind.
- Stopping there would find only half of them. You can also fold along a line joining the midpoints of opposite edges.
- There are 6 edges too, giving another 3 lines.
- Altogether 3 + 3 = 6. A regular 6-gon has exactly 6 lines of symmetry — the same as its number of corners.
Answer 6
More "Count" problems
- How many turns does the small circle make?
- How many cubes have 2 painted faces?
- Into how many pieces do 4 lines cut the paper?
- In how many ways can the three chosen rods form a triangle?
- How many triangles are there in the figure?
- How many squares are there altogether?