Comparing Angles After Folding a Rectangle

8/10Parametrizationsolid geometry

Problem

figure

As shown in the figure, rectangle ABCDABCD is folded along its diagonal BDBD, carrying triangle ABDABD to triangle ABDA'BD, where AA' does not lie in the plane of the rectangle. (In the figure, AA denotes the original position of the folded vertex.) Let α\alpha denote the angle between the skew lines CDCD and ABA'B. Determine, with proof, which of the following claims must be true:

1. α<ACD\alpha<\angle A'CD 2. α>ACD\alpha>\angle A'CD 3. α<ACA\alpha<\angle A'CA 4. α>ACA\alpha>\angle A'CA

Answer

Solution

Difficulty8/10
TopicsParametrization, solid geometry

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