How to find dihedral angles? Please explain all the methods in detail.

The following methods are used to find the dihedral angle:

1. Vertical plane method: Draw a plane perpendicular to the edge, then the intersection of the vertical plane and the dihedral angle is formed The angle is the plane angle of the dihedral angle

2. Definition method: Take a point A on the edge, and then draw perpendiculars through point A on the edge in two planes. Sometimes you can also draw the vertical lines of the edges in two planes, and then draw the parallel line of the other vertical line through one of the vertical feet.

3. Area projection theorem: The cosine value of the dihedral angle is equal to the ratio of the area of ??the projection of a certain half-plane on the other half-plane and the area of ??the plane itself. That is, the formula cosθ=S'/S. The key to using this method is to find the slope polygon and its projection on the relevant plane from the figure, and their areas are easy to find.

Extended information:

1. The properties of dihedral angles are:

1. Any two plane angles of the same dihedral angle are equal. The plane angle of a large dihedral is larger.

2. The plane angle corresponding to the sum or difference of two dihedral angles is the sum or difference of the plane angles corresponding to the original two dihedral angles.

3. A dihedral angle can be bisected, and the bisector plane is unique.

4. The dihedral angles of opposite edges are equal.

2. Construct the plane angle of the dihedral angle:

1. Use the midpoint of the base of an isosceles (including equilateral) triangle to make the plane angle.

2. Use the perpendicular to the surface (the three perpendicular theorem or its converse theorem) to calculate the plane angle.

3. Use the straight line perpendicular to the edge to draw the plane angle through the vertical surface of the edge.

4. Use two parallel lines without edge dihedral angles to make plane angles.

Baidu Encyclopedia-Dihedral Angle