1. Fold the chart along a straight line. If the parts on both sides of a straight line can completely overlap, then this graph is called an axisymmetric graph. This straight line is its axis of symmetry. At this time, we also say that this figure is symmetrical about this straight line (axis).

2. Fold the chart along a straight line. If it can completely coincide with another figure, the two figures are said to be symmetrical about this line. This straight line is called the axis of symmetry. The point that overlaps after folding is the corresponding point, which is called the symmetrical point.

3. The difference and connection between axisymmetric figure and axisymmetric figure.

4. The properties of axisymmetric graphs and axisymmetric graphs

① Two figures symmetrical about a straight line are conformal.

(2) 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.

③ The symmetry axis of an axisymmetric figure is the median vertical line of a line segment connected by any pair of corresponding points.

(4) 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.

⑤ Two figures are symmetrical about a straight line. If their corresponding line segments or extension lines intersect, then the intersection point is on the axis of symmetry.

Second, the vertical line of the line segment

1. Definition: A straight line passing through the midpoint of a line segment and perpendicular to this line segment is called the median line of this line segment, also called the median line.

2. Property: The distance between the point on the vertical line of the line segment and the two endpoints of the line segment is equal.

3. Judgment: The point where the distance between the two ends of a line segment is equal is on the middle vertical line of the line segment.

Third, use coordinates to express the axisymmetric summary:

1. In the plane rectangular coordinate system

(1) The abscissas of the points symmetrical about the X axis are equal, and the ordinate is reciprocal;

(2) The abscissas of the points symmetrical about the Y axis are opposite to each other, and the ordinate is equal;

③ The abscissa and ordinate of a point symmetrical about the origin are opposite numbers;

(4) the horizontal (vertical) coordinate relationship between two points on a straight line parallel to the X axis or the Y axis;

⑤ About the coordinates symmetrical to the straight line X=C or y = c.

The coordinates of the point (x, y) on the axis symmetry of X are _ (x,-y) _ _ _.

The coordinate of the point where the point (x, y) is symmetrical about y is _ _ (-x, y) _.

2. The perpendicular lines of the three sides of a triangle intersect at a point, and the distance from the point to the three vertices of the triangle is equal.

Fourth, (isosceles triangle) knowledge review

1. Properties of isosceles triangle

① The two base angles of an isosceles triangle are equal. (equilateral and angular)

② The bisector of the top angle of the isosceles triangle, the median line on the bottom edge and the height on the bottom edge coincide. (three in one)

Understanding: Knowing one line of an isosceles triangle can infer the other two lines.

2. Determination of isosceles triangle;

If the two angles of a triangle are equal, then the opposite sides of the two angles are equal. (Equiangular and Equilateral)

Five, (equilateral triangle) knowledge review

1. Properties of equilateral triangles:

Three angles of an equilateral triangle are equal, and each angle is equal to 600.

2. Determination of equilateral triangle;

A triangle with three equal angles is an equilateral triangle.

② An isosceles triangle with an angle of 600 is an equilateral triangle.

3. In a right triangle, if an acute angle is equal to 300, then the right side it faces is equal to half of the hypotenuse.