Q:

# How many lines of symmetry does a triangle have?

A:

The number of lines of symmetry a triangle has depends on the type of triangle. An equilateral triangle has three lines of symmetry, while an isosceles has one line of symmetry, and a scalene triangle has none.

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Credit: dgrosso23 CC-BY 2.0

For any triangle, a line of symmetry must bisect an angle and the side opposite that angle, dividing the triangle into two equal right triangles. For this to be true, the original triangle must have at least two equal sides. For an isosceles triangle, the line of symmetry bisects the obtuse angle and the side opposite it. For an equilateral triangle, since all sides and angles are equal, the lines of symmetry can bisect any of the angles. Since a scalene triangle has no equal sides or angles, it can have no lines of symmetry.

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