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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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Q: Why does a triangle with line symmetry have to be isosceles?
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An isosceles triangle has 1 vertical line of symmetry


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