Translation, rotation and folding are three basic transformations in geometric transformation. The so-called geometric transformation is to change the position of a given figure (or part of it) according to certain rules, and then analyze the relationship between related figures in the new figure. Throughout the past few years, the senior high school entrance examinations all over the country have intensified their examination in this area, especially the 20 18 senior high school entrance examination, and the scores in this part have been greatly improved compared with the previous two years.

In order to help you master this part of knowledge, today we will talk about rotation.

Definition of rotation

Several common models

Examples of Rotation Type Themes

1, regular triangle

In positive Δ ABC, p is a point within Δ ABC, and ABP rotates 60 counterclockwise around point A, so that AB and AC coincide. After such a rotation change, the three lines of PA, PB and PC (1- 1-a) in the figure are concentrated in a δ P CP (1-1-b) in the figure, and δδP AP is also a regular triangle.

Example 1 as shown in the figure (1- 1). Let p be a point in the equilateral Δ Δ ABC, PA=3, PB=4, PC=5, and the degree of ∠APB is _ _ _ _ _.

Step 2 be square

In the square ABCD, P is a point in the square ABCD, and ABP rotates 90 clockwise around point B, so that BA and BC coincide. After rotation, the three line segments of PA, PB and PC in Figure (2- 1-a) are concentrated at CPP in Figure (2- 1-b), where CPP is an isosceles right triangle.

Example 2 is shown in Figure (2- 1), where P is a point in the square ABCD, and the distances from the point P to the three vertices A, B and C of the square are PA= 1, PB=2 and PC=3, respectively. Find the square ABCD area.

3, isosceles right triangle

In the isosceles right triangle Δ ABC, ∠ c = 90, and p is a point within Δ ABC. Rotate APC 90 counterclockwise around point C to make AC and BC coincide. After this rotation, aδδP CP in Figure (3- 1-b) is an isosceles right triangle.

Example 3 is shown in the figure. In Δ ABC, ∠ ACB = 90, BC=AC, P is the point in Δ ABC, PA=3, PB= 1, PC=2. Find the degree of ∠BPC.

Summary:

Rotation is the basic transformation in geometric transformation. Generally, a given graph or part of it is rotated to get a new combination, and then the relationship between related graphs is analyzed in the new graph, thus revealing the internal relationship between conditions and conclusions and finding out the way to prove the problem.