Chapter 6, Problem 12RP

Solution

To Prove: Any point on the perpendicular is equidistant from the vertices of the square.

Given information: A line is drawn perpendicular to the plane of a square at the point of intersection of the square’s diagonals is provided in the question which will help to find the solution.

  

Proof: Here, we have been joined O’A and O’D

Here, BD = AC (diagonals are equal in squares)

And, AO = OC, OB = OD (intersects at mid-point)

So that, if we take O’A = O’D (O’ is any point on line perpendicular to plane)

Hence, AO = AO’ (any point on line perpendicular to plane is equidistant from vertices)