# Theorem of three perpendiculars

 Let [color=#c51414] P[/color] be a point on the plane [color=#555]$\alpha$[/color]. Draw the line [i]r[/i], perpendicular to plane [color=#555]$\alpha$[/color] in [color=#c51414] P[/color], then a new line [color=#c51414][i]t[/i][/color] in the same plane. Now draw the line [color=#1551b5][i]s[/i][/color], perpendicular to [color=c51414][i]t[/i][/color] through [color=#c51414]P[/color]. Finally draw the plane [color=#1551b5]$\beta$[/color], through [i]r[/i] and [color=#1551b5][i]s[/i][/color]. Then the plane [color=#1551b5] $\beta$[/color] is perpendicular to line [color=c51414][i]t[/i][/color]. Move the points in the construction and see how the position of planes and perpendicular lines modify accordingly.