How many lines of symmetry does an equilateral triangle have?
- 0 lines of symmetry
- 1 line of symmetry
- 2 lines of symmetry
- 3 lines of symmetry (correct answer)
Explanation: This question tests understanding of symmetry in equilateral triangles (CCSS.4.G.3: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts). A line of symmetry is a line that divides a figure into two identical halves that are mirror images of each other. An equilateral triangle has exactly 3 lines of symmetry, each running from a vertex (corner) to the midpoint of the opposite side—when you fold along any of these lines, the two resulting triangular halves match perfectly because all sides and angles in an equilateral triangle are equal. Students often think triangles have only 1 line of symmetry because they're used to seeing isosceles triangles, which indeed have just one line from the vertex angle to the base. The key distinction is that equilateral triangles have three equal sides and three equal angles, creating three-fold symmetry. To help students visualize this, have them cut out equilateral triangles and test all three possible vertex-to-midpoint folds, marking each line of symmetry with a different color. Compare this with isosceles triangles (1 line) and scalene triangles (0 lines) to reinforce how the number of equal sides relates to the number of symmetry lines.