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No such thing as a regular triangle. You need to be more accurate in your triangular description. Equilateral triangle is symmetric about three lines of symmetry. Isosceles triangle is symmetric one line of symmetry. Right-angled, and Scalene triangles have no lines of symmetry.
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YES!!! An equilateral triangle has three lines of symmetry. They are drawn from any one corner to the opposite base. They should all intersect at the centre of the triangle. By comparison, an Isosceles triangle has only one line of symmetry. From the one unequal angle to the opposite side. Right angled, and scalene triangles do not have lines of symmetry.
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You cannot. An equilateral triangle has 3 lines of symmetry, an isosceles has one and a scalene none. So there is no triangle with two lines of symmetry. Of course, you could draw only two of the three possible lines of symmetry for an equilateral triangle.