What is the axis of symmetry?

Symmetry axis, a mathematical term, refers to a straight line, which refers to the axial symmetry or rotational symmetry of geometric figures. One part of a symmetrical figure rotates around it for a certain angle and then coincides with another part. Many figures have axes of symmetry. For example, an ellipse or hyperbola has two axes of symmetry and a parabola has one axis of symmetry. The symmetry axis of a right cone or a right cylinder is a straight line passing through the center of the bottom surface and the vertex or the center of another bottom surface.

Firstly, the concept of point symmetry of a straight line is introduced: if point A and point B are on both sides of the straight line and are perpendicular to the middle line of segment AB, they are said to be symmetrical about the straight line, and point A and point B are called symmetrical points about the straight line, and the straight line is called symmetrical axis.

Definition one

On the plane, if all points of figure F are symmetrical about a straight line on the plane, the straight line is called the symmetry axis under the figure.

Definition 2

On the plane, if there is a straight line, all the points in Figure F are symmetrical points about the straight line. If it is still the figure F itself, it is called an axisymmetric figure, and the straight line has its own axis of symmetry.

Common axisymmetric graphics:

Several common axisymmetric and centrosymmetric figures;

Axisymmetric graphics: line segment, angle, isosceles triangle, equilateral triangle, diamond, rectangle, square, isosceles trapezoid, circle, hyperbola (with two symmetry axes), ellipse (with two symmetry axes), parabola (with one symmetry axis), etc.

Number of symmetry axes: an angle has a symmetry axis, that is, the straight line where the bisector of the angle of the angle lies; The isosceles triangle has an axis of symmetry, which is the median vertical line of the base; An equilateral triangle has three axes of symmetry, that is, the median vertical lines on three sides; A diamond has two symmetry axes, which are straight lines where two diagonals are located, and a rectangle has two symmetry axes, which are straight lines between two groups of opposite sides.

Centrally symmetric figures: line segments, parallelograms, diamonds, rectangles, squares, circles, etc.