1. Axisymmetric graph 1. Axisymmetric figure If a figure is folded along a straight line, the parts on both sides of the straight line can completely overlap. This figure is called an axisymmetric figure, and this straight line is its axis of symmetry. 2. Two figures are symmetrical about a straight line. Fold a graph along a straight line. If you can, if you can overlap another graph, then the two graphs are said to be symmetrical about this straight line. This straight line is called symmetry axis, and the overlapping point after folding is the corresponding point, which is called symmetry point. 3. The essence of axial symmetry 1 If two figures are symmetrical about a straight line, then the axis of symmetry is the median vertical line taken by the straight line connecting any pair of corresponding points. ② The symmetry axis of an axisymmetric figure is the median vertical line taken by a straight line connecting any pair of corresponding points. 4. The nature of the midline of a line segment ① The distance from the point on the midline (midline) to the two endpoints of this line segment is equal. ② The point with the same distance from the two endpoints of a line segment is on the bisector (median vertical line) of this line segment. 2. Make an example of an axisymmetric figure: Make point A symmetrical about point B. Practice: Draw an arc with the center of a and b and the length greater than -AB as the radius, intersect with C and D, and connect CD. Then a straight line is demand. 3. Coordinate symmetry 1. On the coordinate characteristics of X: 2 symmetrical points. The coordinate characteristics of Y-symmetric points: the abscissa remains unchanged. The ordinate is the same, but the abscissa is the opposite. 3. If two points (x, y) and (x, y) are symmetrical about the straight line x = m 4. If two points (x, y) and (x, y) are symmetrical about the straight line y = n 4. Isosceles triangle 1. Properties of isosceles triangle: ① The base angles of isosceles triangle are equal (referred to as "equilateral corners"). 2. Determination of equilateral triangle If a triangle has two equal angles, then the opposite sides of the two angles are also equal ("equilateral" for short) 5. Equilateral triangle 1. A triangle with three equilateral sides is called an equilateral triangle. 2. All three internal angles of an equilateral triangle are equal. Each angle is equal to 60 3. An equilateral triangle is an equilateral triangle. 4. An isosceles triangle with an angle of 60 is an equilateral triangle. In a right triangle, if an acute angle is equal to 30, then the right side it faces is equal to half of the hypotenuse.