Angle finding method of solid geometry

There are two types of problems that are the most important in the college entrance examination of solid geometry. One is the proof of parallelism and verticality; The second is to find the angle. The problem of finding the angle is divided into three categories: 1) Finding the angle formed by two straight lines on different planes. 2) Find the included angle between the straight line and the plane. 3) Find the dihedral angle.

Methods: Firstly, according to the definitions of line angle, line angle and dihedral angle, the plane angles of line angle, line angle and dihedral angle are calculated by using the conventional method of solid geometry, and then calculated in a triangle. The second is to establish a coordinate system and use the space vector method to find the angle.

1. Find the angle formed by two straight lines on different planes: the angle ranges from 0 degrees to 90 degrees, excluding 0 degrees and including 90 degrees. The method is that one straight line does not move, and the other straight line moves in parallel and intersects with the previous straight line. The acute angle or right angle formed by them is the angle formed by two straight lines in different planes, and then it is put into the triangle where it is located to solve the triangle and find out the size of the angle. Of course, you can also take another point in geometry, move two straight lines in parallel and intersect, and then find the angle.

When you meet the diagonal of a cube, you usually fill a cube with the same size by complement method, and then move the straight line in parallel.

Error-prone point: If the topic setting conditions tell you the angle formed by two straight lines on different planes, there should be two situations in the graph, this angle or its complementary angle.

2. Find the angle between the straight line and the plane: the angle ranges from 0 degrees to 90 degrees, excluding 0 degrees and including 90 degrees.

Methods include definition method, equal volume method and shape filling method.

Constant volume method model: when a point is perpendicular to a plane, if the vertical foot is difficult to determine, the length of the vertical line segment, that is, the height line, is directly determined by constant volume method, and then the height line length is put into a right triangle to find the angle.