Given a cube ABCDA1B1C1D1. Prove that AC1 is perpendicular to BD.
| September 4, 2021 | education
Since the figure is a cube, all of its faces are squares.
In the square ABCD, construct the diagonals AC and BD, which intersect at right angles.
AC is perpendicular to BD.
The side faces of the cube are perpendicular to the planes of its bases, then CC1 is perpendicular to AC.
AC is the projection of the AC1 diagonal onto the base plane, and since AC is perpendicular to BD, then PC1 is also perpendicular to BD, which was required to be proved.
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