1 positional relationship (definition)

Intersection: There is only one thing in common.

Parallel: There is nothing in common on the same plane.

Different planes: Different planes have nothing in common.

Axioms and inferences should be memorized

3 test site-the angle formed by straight lines in different planes ① → right angle→ common vertical line (perpendicular intersection) → the distance between straight lines in different planes.

① Method: Select points (commonly used: endpoints and midpoints).

Translation (spatial straight line planarization)

Also pay attention to summing up the theorems introduced in the usual exercises, which can save time when making choices to fill in the blanks.

Double-line surface problem

1 positional relationship (definition)

The straight line is in the plane: there are countless things in common.

Out-of-plane straight lines: ① Intersection: There is only one common point.

② Parallel: Nothing in common.

2-line plane parallelism

(1) definition,

② Decision theorem: If A is not included in α, B is included in α, and a‖b is a‖α.

③ property theorem: if a‖α, a is included in βα∪β= b, then a‖b (line-plane parallel → line-line parallel).

3. Vertical lines and planes

Ⅰ. Parallelism is similar to ① definition, ② judgment, ③ nature → distance between points and surfaces.

Ⅱ Diagonal projection ①→ Angle between straight line and plane

(1) projection, slash, etc.

Slant lines, projections, etc.

The shortest vertical line segment

Ⅲ Three Vertical Theorems and Inverse Theorems

Trilateral problems are similar to linear problems, so leave it to yourself to sort out ~

* When learning solid geometry, we can use some models (cubes, cuboids, spatial quadrangles, triangular pyramids, etc. ) to help us remember axioms and theorems. Especially when judging true and false propositions, you can find counterexamples in these models to help you judge.