Perpendicular and slant, line–plane angle, dihedral angle
Find a slant from the perpendicular and its projection, measure the angle between a line and a plane and a dihedral angle by its linear angle, then show that two planes are perpendicular.
- Palestine: grade 11
- Ukraine: grade 10
- Russia: grade 10
Guide
This follows the Ukrainian Grade 10 geometry course (§35–37): the synthetic method with projections and the linear angle of a dihedral angle, not vectors.
The solid is the box ABCDA₁B₁C₁D₁ with base ABCD. Turn it to see where a right angle really is.
Common slips: adding the perpendicular and the projection instead of using Pythagoras, taking an angle in the base for the angle between a line and a plane, and thinking two planes are perpendicular just because they meet.