Diagonal of a cube

Two triangular sections of a cube cut its diagonal into 3 parts as shown below. Is the diagonal cut into 3 equal parts? Is the diagonal perpendicular to the triangular sections? Try to drag a figure to get a better view for tackling this problem.

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press right mouse button and drag to freely rotate the entire figure

This question is suggested by Mr. Yuen Wah Kong and discussed in a workshop on April 29, 2006, organised by the Hong Kong Association for Science and Mathematics Education.