How many ways can a pair be chosen from lines n, p, q, and r?
6
Practice makes perfect
Any rectangle formed by the lines on the diagram needs to have two pairs of parallel sides. We will proceed assuming that the two types of parallel lines are perpendicular.
One pair of sides must be on lines l and m.
For the other pair of sides, we can pick any two of lines n, p, q, and r.
If one of the sides is on line n, then we have three possibilities.
If none of the sides is on line n and one of the sides is on line p, then we have two possibilities.
If none of the sides is on line n or p, then we have one possibility.
Altogethere there are six rectangles formed by the intersecting lines.
Please be aware of the fact that if the lines are not actually perpendicular, there are no rectangles in the figure.
