Counting Perpendicular Lines: Analysis of Nested Square Geometry

Question

Determine how many pairs of perpendicular lines are there in the two squares shown below:

00:00 How many perpendiculars are there in the drawing?

00:03 All angles in the square are right angles

00:07 A perpendicular creates a right angle at the intersection point between the lines

00:12 Let's mark and count all the right angles

00:24 And this is the solution to the question

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

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