Translation, rotation and axial symmetry are three basic congruent transformations. If the transformed figure coincides with the original figure, that is, the shape and size of the figure remain unchanged, then the transformation of this figure is called congruent transformation, which is essentially the same distance between two points on the plane. In other words, in the original picture, if the distance between any two points is L, then the distance between the two points after the transformation is still L, so the congruence transformation is distance-preserving transformation, that is, distance-preserving transformation. After keeping the distance, it can be proved that the shape and size of natural graphics are still maintained. In fact, we can intuitively think about how two overlapping graphs move from one graph to the other. Let's take a triangle as an example. First, we can translate to a certain position, or a vertex of the triangle can overlap. Another case is that the order of vertices is reversed, and then two graphics need to be reflected (folded, axisymmetric) to overlap. The above transformations are what we call translation, rotation and axisymmetric transformations, which are three basic congruent transformations. What are translation, rotation and reflection? Instead of giving a strict mathematical definition, we give an intuitive explanation and point out the basic elements of these transformations. As shown in the above figure, if any point in the original figure is connected with the corresponding point in the new figure in the same direction and length, such congruence transformation is called translation transformation, which is called translation for short. In other words, the basic feature of translation is that "the connecting lines of each point and its corresponding point are parallel and equal" before and after graphic translation. Obviously, determining the translation transformation requires two elements: direction and distance. For translation, please note: 1. 2. Direction: In what direction does translation take place; 3. Distance: How far has it been translated? As shown in the above figure, the basic feature of rotation is that "the distance between the corresponding points and the rotation center is equal before and after the rotation of the figure, and the included angle between each group of corresponding points and the rotation center is equal to the rotation angle". Obviously, determining the rotation transformation requires two elements: the rotation center and the rotation angle (belt direction). For rotation, please specify: 1. Basic graphics: What graphics have been rotated? 2. Center of rotation: around which point to rotate; 3. Direction: What direction, clockwise or counterclockwise; 4. Angle: By the way, the center of rotation is not necessarily the vertex on the basic diagram, but any point on the plane. Some teachers think that the center of rotation is the vertex of the figure, which is wrong. If the line segment connecting each group of corresponding points in the new image and the original image is perpendicular to the same straight line and is divided into two by the same straight line, such congruence transformation is called reflection transformation. A line that bisects the line segments connected by symmetrical points vertically is called the symmetry axis. That is, the basic feature of reflection transformation is that "the line segment connecting any group of corresponding points is vertically bisected by the axis of symmetry". Obviously, the key to determine the reflection transformation is to find the symmetry axis. If you don't find the resources you need, you can find them in the relevant sections of the forum or post them for help. Friendly reminder: click here to see more courseware, videos, lesson plans, tutors, illustrations …