If a figure is folded in half along a straight line and the two parts completely overlap, such a figure is called an axisymmetric figure, and this straight line is called an axis of symmetry.

for instance

For example, isosceles triangle, square, equilateral triangle, isosceles trapezoid, circle and regular polygon are all axisymmetric figures. Some axisymmetric figures have more than one axis of symmetry. A circle has countless symmetry axes, and a straight line with the diameter of each circle is the symmetry axis of the circle.

nature

The symmetry axis is a straight line!

A straight line perpendicular to and bisecting a line segment is called the perpendicular bisector of the line segment, or the vertical centerline. The point on the vertical line in the line segment is equal to the distance between the two ends of the line segment.

In an axisymmetric figure, the distance between the opposite points on both sides of the axis of symmetry is equal.

Axisymmetric graphs are congruent.

If two figures are symmetrical about a straight line, then the symmetry axis is the middle perpendicular of the line segment connected by any pair of corresponding points.

After rotating 180 degrees, it coincides with the original drawing.

Graphic symmetry

Theorem and its inverse theorem

Theorem 1: Two graphs symmetric about a straight line are conformal.

Theorem 2: If two figures are symmetrical about a straight line, then the symmetry axis is the perpendicular line connecting the corresponding points.

Theorem 3: Two figures are symmetrical about a straight line. If their symmetry axes or extension lines intersect, then the intersection point is on the symmetry axis.

Theorem 3 Inverse Theorem: If the straight line connecting the corresponding points of two graphs is vertically bisected by the same straight line, then the two graphs are symmetrical about this straight line.