The straight line is called the symmetry axis, and the symmetry axis is represented by the dotted line; At this time, we also say that this figure is symmetrical about this line. Such as circle, square, isosceles triangle, equilateral triangle, isosceles trapezoid, etc.
I. Examples
For example, isosceles triangle, square, equilateral triangle, isosceles trapezoid, circle and regular polygon are all axisymmetric figures. A circle has countless symmetry axes, all of which are straight lines passing through the center of the circle.
Pay special attention to the line segment, which has two symmetry axes, one is the straight line where the line segment is located and the other is the middle vertical line of the line segment.
Capital letters a, b, c, d, e, h, etc.
Second, nature.
1. The symmetry axis is a straight line.
2. In an axisymmetric figure, the distance between the corresponding points on both sides of the axis of symmetry is equal.
3. Axisymmetric graphics, folded in half along the axis of symmetry, and completely overlapped left and right.
4. If two figures are symmetrical about a straight line, then this straight line is the line segment whose symmetry axis bisects the symmetry point vertically.
5. Graphic symmetry? .
Third, the 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 the axis of symmetry intersects the extension lines of two symmetrical line segments, the intersection point is on the axis of symmetry.
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.
Fourth, the role of life.
1, for beauty. For example, Tiananmen Square is symmetrical and beautiful.
2. Keep balance. Like the wings of an airplane.
3, the needs of special work. For example, the five-pointed star, paper cutting.
The concept of verb (abbreviation of verb) difference
To distinguish these two concepts, it should be noted that axisymmetric graphics must be folded along a straight line, and the parts on both sides of the straight line overlap each other. The key point is to grasp two points: one is to fold along a straight line, and the other is to overlap each other; A centrosymmetric figure is that the figure rotates around a certain point180 and coincides with the original figure. The key is to grasp two points: one is to rotate around a certain point, and the other is to coincide with the original figure. In practical differences, axisymmetric graphics should be folded like origami, and what can overlap is axisymmetric graphics; Centrally symmetric graphics only need to be inverted to see if there is any change. What hasn't changed is the figure with central symmetry. At present, the common figures in primary school textbooks are classified as follows: the figures that are both axisymmetric and centrally symmetric are: rectangle, square, circle, diamond and so on.
Only axisymmetric figures are: angle, pentagram, isosceles triangle, equilateral triangle, isosceles trapezoid and so on.
Only the figure with central symmetry is a parallelogram.
Figures that are neither axisymmetric nor centrosymmetric include equilateral triangles, isosceles trapezoid, etc.
A graph is both symmetric and central. There must be two or more axes of symmetry.