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例题如图。AB是圆0的直径,PA垂直于圆0所在的平面,C是圆周上一点,求证:△PAC所在的平面垂直于△PBC所在的平面。错证∠ACB是半圆上的圆周角BC⊥AC,AC是PC在平面ABC上的射影BC⊥PC(三垂线定理)BC⊥平面PAC平面PBC⊥平面PAC。错处 BC⊥PCBC⊥平面PAC属循环论证。错因忽略了三垂线定理的证明。颠倒了推理的逻辑顺序。现借助上图,重温三垂线定理的证明:
Sample questions as shown. AB is the diameter of circle 0, PA is perpendicular to the plane where circle 0 is located, and C is a point on the circumference. Verify that the plane of △PAC is perpendicular to the plane of △PBC. The false positive ACB is the circumferential angle BC ⊥ AC on the semicircle, and AC is the projective BC ⊥ PC (triple vertical line theorem) BC plane PAC plane PBC ⊥ plane PAC on the plane ABC. The wrong place BC⊥PCBC⊥planar PAC is a cyclical demonstration. The error ignores the proof of the triple vertical. Reversed the logical sequence of reasoning. Now with the help of the above figure, revisit the proof of the three vertical line theorem: