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.
Fourthly, the symmetry method.
1, find out the key points of the given graph.
2. Find the distance between the key point of the figure and the symmetry axis.
3. Find the symmetry point of the key point.
4. Connect these points in the order of the given graph.
Five, painting methods
1, find a pair of symmetric points of the graph.
2. Connect the symmetrical points.
3. Pass through the midpoint of this line segment as the vertical line of this line segment.
Judgment of intransitive verbs
A straight line that passes through the midpoint of a line segment and is perpendicular to the line segment is called the midline of the line segment. In this way, the following characteristics can be obtained:
1. If two figures are symmetrical about a straight line, then the symmetry axis is the perpendicular to the line segment connected by any pair of corresponding points.
2. Similarly, the symmetry axis of an axisymmetric figure is the median vertical line of a line segment connected by any pair of corresponding points.
3. The distance between the point on the vertical line of the line segment and the two endpoints of the line segment is equal.
4. Symmetry axis is the set of points with equal distance to both ends of the line segment.