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2003年全国高考数学新、旧课程卷(文科)第15题:在平面几何里,有勾股定理“设△ABC 的两边AB、AC 互相垂直,则 AB~2+AC~2=BC~2。”拓展到空间,类比平面几何的勾股定理,研究三棱锥的侧面面积间的关系,可以得出的正确结论是:“设三棱锥 A-BCD的三个侧面 ABC、ACD、ADB 两两互相垂直,则 S_(△ABC)~2+S_(△ACD)~2+S_(△ADB)~2=S_(△BCD)_~2.”该题把平面几何中直角三角形三边之间的关系
In 2003, the National Mathematical Examination New and Old Course Volume (Liberal Arts) Question 15: In Plane Geometry, there is the Pythagorean Theorem. “By setting ABC, the two sides AB and AC are perpendicular to each other, then AB~2+AC~2=BC~2 “Expanding into space, analogous to the Pythagorean theorem of plane geometry, and studying the relationship between the lateral areas of a triangular pyramid, the correct conclusion that can be drawn is: ”Set the three sides of the triangular pyramid A-BCD ABC, ACD, ADB two When perpendicular to each other, S_(△ABC)~2+S_(△ACD)~2+S_(△ADB)~2=S_(△BCD)_~2.”) Relationship