Difficult geometry problem

bator

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Nov 15, 2021
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IMG_20211115_174852.jpg
ABCD is a square with a side length of 1. A set of parallel lines with distance 1 between them overlap the square. P, Q, R and S are the points of intersection resulted from the overlapping.
Find theta.

I've realized that the opposite figures inside the square are similar, and have tried substituting different lengths with x and y but nothing seems to work.

Help would be appreciated, thanks!
 

Cubist

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Oct 29, 2019
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Have you posted the whole question? I think the value of θ depends on the angle between the lines AB and PQ.
 

lev888

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Jan 16, 2018
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Have you posted the whole question? I think the value of θ depends on the angle between the lines AB and PQ.
Sketching in CAD produced the same 45 degree θ for multiple angles between AB and PQ.
 

blamocur

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Oct 30, 2021
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Hint: in the attached drawing consider triangles BDF and ACG
 

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lev888

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View attachment 29724
ABCD is a square with a side length of 1. A set of parallel lines with distance 1 between them overlap the square. P, Q, R and S are the points of intersection resulted from the overlapping.
Find theta.

I've realized that the opposite figures inside the square are similar, and have tried substituting different lengths with x and y but nothing seems to work.

Help would be appreciated, thanks!
Any progress?
 
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