The basis of symmetry is that everything on one side of an imaginary line is the same as the other. This means that if you split a triangle down the middle by an imaginary line, one side of the triangle on both halves will be the same. This defines an isosceles triangle. An equilateral triangle also has line symmetry.
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An isosceles triangle has 1 vertical line of symmetry
An Isosceles triangle has at least one line of symmetry but if it has more than one line of symmetry it can be an Equilateral triangle as well as a Isosceles Triangle. So a triangle with one line of symmetry is always Isosceles and If it has more than one it is always an Equilateral triangle as well as an Isosceles triangle. Example of an Isosceles triangle:
An isosceles triangle has 1 line of symmetry
An isosceles triangle has two equal sides and one line of symmetry
An isosceles triangle