Counting Perpendicular Lines: Analysis of Nested Square Geometry

Let's remember that perpendicular lines are lines that intersect at a right angle of 90 degrees.

Our right angles are:

$ABC,BCD,CDA,DAB,EFG,FGH,GHE,HEF$

The lines that form angle ABC are: AB+BC

The lines that form angle BCD are: BC+CD

The lines that form angle CDA are: CD+DA

The lines that form angle DAB are: DA+AB

The lines that form angle EFG are: EF+FG

The lines that form angle FGH are: FG+GH

The lines that form angle GHE are: GH+HE

The lines that form angle HEF are: HE+EF

Since we have 8 marked right angles of 90 degrees in the squares, we must have 8 pairs of perpendicular lines.