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下面三题都是高中《立体几何(必修)》教材中的习题. 题目1 如图,AB和平面α成的角是θ_1,AC在平面α内,AC和AB的射影AB′,所成角为θ_2,设么∠BAC=θ.求证: cosθ_1·cosθ_2=cosθ.(P.117第3题) 题目2 经过一个角的顶点引这个角所在的平面的斜线.如果斜线和这个角两边的夹角相等,那么斜线在平面上的射影是这个角的平分线所在的直线.
The following three questions are the exercises in the high school “Three-Dimensional Geometry (Compulsory)” textbook. Question 1 As shown in the figure, the angle formed by AB and plane α is θ_1, and the angle AC is in the plane α, the projection AB’ of AC and AB. For θ_2, set ∠ BAC = θ. Proof: cosθ_1 · cosθ_2 = cosθ. (P.117, item 3) Problem 2 Follow the vertice of a corner to refer to the slash of the plane where the angle lies. If the slashes and both sides of the angle The angles are equal, then the projection of the slash on the plane is the straight line where the bisector of this angle lies.