Segment OS is drawn from the center O of the square ABCD perpendicular to its plane. a) Find the lines perpendicular

Segment OS is drawn from the center O of the square ABCD perpendicular to its plane. a) Find the lines perpendicular to the line BD. b) Prove that the line AC is perpendicular to the plane SВD. 2. How to check using measurements, is the line perpendicular to the floor along which two adjacent walls of the room are connected?

a. BD – the diagonal of the square ABCD, the diagonals of the square intersect at right angles, hence AC is perpendicular to BD. By condition, OS is perpendicular to the plane of the square ABCD, which means it is perpendicular to any straight line in this plane, including BD.
Answer: straight AC and OS are perpendicular to BD.

b. A straight line is perpendicular to a plane if it is perpendicular to any straight line lying on this plane. According to our condition, the line OS is perpendicular to the plane of the square ABCD, which means it is perpendicular to all lines on this plane: OS⊥AB, AD, AC, AO, BC, BD, BO, CD, CO. It turns out OS⊥AC, which means that AC⊥OS means AC⊥SBD.

v. There are two ways to determine if a wall-to-floor connection line is perpendicular:
1. If we consider that the walls themselves are perpendicular to the floor, then put a segment of 30 cm on one of the walls, and a segment of 40 cm long on the line of joining the walls, then according to the Pythagorean theorem, if we measure the distance along the wall between these points, we should get 50 cm …
2. You can set aside a distance of 40 cm on the floor, and 30 cm on the wall connection line, then the air distance between the points according to the Pythagorean theorem is 50 cm. (You can postpone other distances, but these are easier to calculate.)