|The red lines represent the lines of symmetry|
There are three types of triangles: Equilateral, Isosceles and Scalene triangles.
All three angles and sides of an equilateral triangle are equal. Thus, an equilateral triangle has three lines of symmetry, each passing through the midpoint of a side and the opposite vertex.
In an Isosceles triangle, two sides and their included angles are equal in measure. This implies that if you draw a line through the third, distinct angle, and extend it through the mid point of the opposite side, then the two parts so formed will have two corresponding equal sides and two corresponding equal angles. Drawing a line through any of the two equal angles will not result in symmetrical intersection of the triangle, and hence an isosceles triangle has only one line of symmetry.
A scalene triangle has all distinct angles and sides, and therefore, it does not have any line of symmetry.
The above figure shows each of the above mentioned triangles with their respective lines of symmetry.