Concept explainers
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)
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