IV Location of planes in space

Most planes around you are horizontal or vertical. The planes of exercise books, school yards, floors, table tops are horizontal, of walls of rooms, black boards, window panes vertical, of roofs and embankments inclined.

These terms originate from your position in space: If you stand up, the horizontal plane below you extends to the horizon, and vertically above you lies the sky.

Man's preference for horizontal and vertical planes is decided by the fact that bodies tend to slide down inclined planes and that buildings with vertical edges and walls are stable.

If you let a plummet line hang over a horizontal plane and place in an arbitrary direction a ruler below it, the plumb-line and the edge of the ruler are perpendicular to each other, that is, the plumb-line is perpendicular to the plane. This relative location of a line and plane applies also when the plane is not horizontal. Thus, a straight line is perpendicular to a plane, when every line in the plane through its base point is perpendicular to it. Since a plane is defined by two intersecting lines, you have the Rule:

A straight line is perpendicular to a plane, if two straight lines
in the plane through its base point are perpendicular to it

You obtain a model of the respective location of a straight line and a plane by placing two set-squares with one side on a table and let their other sides touch each other.

You can check whether a plane (table top, window shelf or wall) is horizontal by placing a level gauge on the plane. If the bubble locates at the centre of the gauge, the table is horizontal.

If you place a plane through a line perpendicular to a plane,
you say that these planes are perpendicular to each other.

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