Draw the following.
A triangle with exactly one line of symmetry
An isosceles triangle has exactly one line of symmetry. Draw a triangle with two equal sides. The line of symmetry passes from the vertex between the equal sides to the midpoint of the base.
A triangle with exactly three lines of symmetry
An equilateral triangle has exactly three lines of symmetry. Draw a triangle with all three sides equal. Each line of symmetry passes from a vertex to the midpoint of the opposite side.
A triangle with no line of symmetry
A scalene triangle has no line of symmetry. Draw a triangle with all three sides of different lengths. No line can divide it into mirror halves.
Is it possible to draw a triangle with exactly two lines of symmetry?
No, it is not possible to draw a triangle with exactly two lines of symmetry. If a triangle has two lines of symmetry, it must be equilateral and therefore have three lines of symmetry.
Explanation
(a) An isosceles triangle has exactly one line of symmetry - the perpendicular from the vertex to the base. (b) An equilateral triangle has three lines of symmetry, one through each vertex. (c) A scalene triangle has no equal sides and no equal angles, so no line of symmetry exists. (follow-up) The existence of two lines of symmetry in a triangle forces the third line to also be a line of symmetry, making it equilateral.