The classical example of the figure having the center of symmetry is a circle. Any its point is at identical distance from the center. Whether there are types of triangles to which it is also possible to apply this concept?
The symmetry happens two types: central and axial. At the central symmetry any straight line drawn through the center of a figure divides it into two absolutely identical parts which are completely symmetric. Simple words, they are specular reflection of each other. At a circle of such straight lines it is possible to carry out an infinite set, anyway they will divide it into two symmetric parts.
Symmetry axis
The majority of geometrical figures have no such characteristics. It is possible to carry out to them only an axis of symmetry and that not at all. The axis is also a straight line which divides a figure into symmetric parts. But for an axis of symmetry there is only a certain location and if slightly to change it, then the symmetry will be broken.
It is logical that each square has a symmetry axis, at it all parties are equal and each corner is equal to ninety degrees. Triangles are different. Neither the axis, nor the center of symmetry can have triangles which have all different parties. And here in isosceles triangles it is possible to carry out a symmetry axis. Let's remember that the triangle with two equal parties and respectively two equal corners adjacent to the third party - the basis is considered isosceles. For an isosceles triangle an axis will be the straight line passing from triangle top to the basis. In this case this straight line will be at the same time both a median, and a bisector as it will halve a corner and will reach exactly the middle of the third party. If on this straight line to put a triangle, then the turned-out figures completely will copy each other. However in an isosceles triangle the axis of symmetry can be only one. If through its center to draw other straight line, then it will not divide it into two symmetric parts.
Special triangle
The equilateral triangle is unique. It is a special type of triangles which also is isosceles. However, at it each party can be considered as the basis as all its parties are equal, and each corner makes sixty degrees. Therefore, at an equilateral triangle exist the whole three axes of symmetry. These straight lines meet in one point in the center of a triangle. But even such feature does not turn an equilateral triangle into a figure with the central symmetry. The equilateral triangle as through the specified point only three straight lines divide a figure into equal parts has no center of symmetry even. If to draw a straight line in other direction, then the triangle will not have symmetry any more. Means, these figures have only axial symmetry.