math
9th Grade - Spatial geometry

9th Grade lesson

7 - Spatial geometry


You know what a line is, and that a line is infinite. You also know well the lines that belong to the plane too (the ones you can draw on a sheet of paper with a ruler). But there are also lines in space. For example, the top of your computer screen is a line; there is also a line that passes through your right middle finger and the center of the sun. These are spatial lines.

Parallel lines

In the plane, two lines that are not parallel are secant (or transversal). That's not the case in space. For example the line on the right of your computer screen (vertical), and the line on the left of your desk (horizontal) are neither secant nor parallel.
parralel lines

In this cube, the blue lines are parallel, the yellow lines are neither parallel nor secant.

Orthogonal lines

Two lines are orthogonal if there exists a line which is parallel to the first one and perpendicular to the second one.
orthogonal lines

In this cube, the two red lines are orthogonal because the horizontal one and the green line are perpendicular.

Intersections in space

It's easy to imagine that if a line is not parallel to a plane, then the intersection between the line and the plane is a point. And if two planes are not parallel, then their intersection is a line. The roof theorem mentions that if two planes that are not parallel pass through two parallel lines, then the two parallel lines are parallel to the intersection line of the two planes (it draws the roof of a house).


See also : geometry on fmaths.com



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