1. The angle formed by straight lines in different planes is defined by the concept of angle in plane geometry, that is, at any point in space, parallel lines of straight lines in two different planes are drawn respectively. The acute angle or right angle formed by these two straight lines is called the angle formed by two straight lines with different planes, which reflects the positional relationship between the two straight lines with different planes in space and is the basis for studying the two straight lines in space.

2. "Equiangular Theorem" provides the possibility and uniqueness for the definition of the angle formed by two straight lines in different planes, that is, when passing through any point in space, two straight lines are parallel to each other, and the acute angles (or right angles) they form are equal, regardless of the position of the selected point. If the angles formed by straight lines of two different planes are right angles, the straight lines of two different planes are said to be perpendicular to each other.

3. When we talk about the angle formed by straight lines A and B in different planes, we should pass through any point O in the space and quote A '∨A and B '∨B respectively. This involves how to draw parallel lines through any point in space. From the inference 1 of axiom 3 in the Basic Properties of Plane, we can see that there is only one plane after passing a straight line and a point outside it, so

4. Find the angles formed by straight lines on different planes:

(1) Select the appropriate point. Try to choose this point on one of the straight lines of two different planes. )

(2) parallel lines that pass through this point to make straight lines of two different planes (if there are parallel lines or proved parallel lines in the topic, parallel lines are not needed)

(3) Determine the angle formed by two straight lines in different planes.

(4) calculate the angle. (By solving the relationship between the angles of a triangle or a special triangle)

5. The angle formed by two straight lines on different planes is very important knowledge, which requires us to firmly grasp the definition of the angle formed by two straight lines on different planes and the concept that two straight lines on different planes are perpendicular to each other. The angle formed by two straight lines on different planes is a quantity that describes the relative position of two straight lines, and it is converted into the angle formed by the intersection of straight lines to solve it. It should be noted here that the range of angles formed by straight lines of two different planes is 0? & lt≤90? , when =90? When two straight lines on different planes are perpendicular to each other, two straight lines on different planes are perpendicular to each other, and there can be no vertical feet; The key to find the included angle between two straight lines on different planes is to find the angle formed by two straight lines on different planes. The methods to make two straight lines of different planes angle include: translating one of the straight lines to a certain position to make it intersect with the other straight line, or translating two straight lines of different planes to a certain position at the same time to make it intersect. It is worth noting that the angle obtained by intersection after translation must be easy to calculate, so you should choose a suitable position when translating.

6. To find the distance between two straight lines on different planes, first find the common perpendicular of the straight lines on different planes, and then borrow the knowledge of solving triangles to get the answer.