The diagonals of the base of the quadrangular prill pyramid SABCD intersect at point O, point T is the midpoint

| May 28, 2021 | education

The diagonals of the base of the quadrangular prill pyramid SABCD intersect at point O, point T is the midpoint of the edge DC. Prove that the angle OST is equal to the angle between the line OS and the DSC plane.

The planes of the triangles DSC and TSO are perpendicular, since the DSC plane passes through the straight line DC, which is perpendicular to DT perpendicular to TO (TO is parallel to CB) and DT is perpendicular to TS, since in the isosceles triangle DSC (SC = SD) the median ST is simultaneously the height. The line of intersection of these planes (DSC and TSO) passes through points S and T.

The OS projection lies on the ST line, that is, the OST angle is the angle between the OS line and its projection onto the DSC plane, as the angle between the OS line and the DSC plane.



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