The planes of an equilateral triangle ABM and a square ABCD are mutually perpendicular. MK is perpendicular to AB.

The planes of an equilateral triangle ABM and a square ABCD are mutually perpendicular. MK is perpendicular to AB. Which statements are correct: a) MK is perpendicular to BC b) MK is perpendicular to DB c) MВ is perpendicular to DB d) AM is perpendicular to AD

Since the planes of the equilateral triangle ABM and the square ABCD are mutually perpendicular and then the height of the triangle MK is perpendicular to the line of intersection of the planes – the side AB, then it is perpendicular to all the straight lines lying in the plane of the square: a) the straight line MK forms an angle of 90 ° with the straight line BC and the straight lines are crossing ; b) the straight line MK forms an angle of 90 ° with the straight line DB and the straight lines are intersecting; c) straight line MВ  is not perpendicular to DB, since its projection onto the plane forms an angle of 45 ° with the diagonal of the square; d) the straight line AM is perpendicular to the side of the square AD by the theorem of three perpendiculars.