If two non-parallel lines are perpendicular to two other straight lines, each to each. Show that the acute angle between the first pair of lines is equal to the acute angle between the second pair of lines.

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Solution

We say that a pair of lines indicated a, b. The lines are perpendicular to them c, d.

1. Will move one of the parallel lines (c) so as to intersect the point (A) of intersection of a, d and call it c'

2. Then γ=(90−A) (due Right Angled triangle composed of straight a, b, c.

lines A', d). Consequently, $B^{'} = A$ . On the other hand $B^{'} = B$ , since с and c' are parallel.
& β'=90−γ
and hence α = β.

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