# Difficult geometry problem

#### bator

##### New member

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

##### Senior Member
Have you posted the whole question? I think the value of θ depends on the angle between the lines AB and PQ.

#### lev888

##### Elite Member
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.

#### Cubist

##### Senior Member
Sketching in CAD produced the same 45 degree angle for multiple angles between AB and PQ.
Thanks, I'll check my work later.

#### blamocur

##### Full Member
Hint: in the attached drawing consider triangles BDF and ACG

#### Attachments

• d2.pdf
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#### blamocur

##### Full Member
Hint: in the attached drawing consider triangles BDF and ACG
In case someone finds PNG images easier to view than PDF ones:

#### Attachments

• d2.png
71.9 KB · Views: 8

#### lev888

##### Elite Member
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?