Perpendicular Line Identification in Rectangle with Parallel Lines

Question

How many pairs of perpendicular lines are shown in the diagram?

AAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Solution Steps

00:00 How many perpendiculars are there in the drawing?
00:04 A perpendicular creates a right angle at the intersection point between the lines
00:10 Let's mark and count all the right angles
00:39 And this is the solution to the question

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

We will draw straight lines coming from each of the marked points in the figure to examine whether the angles are right angles.

The drawing will look like this:

AAABBBCCCDDDEEEFFFGGGHHH

Note that the lines we drew create right angles, which are:

BAD,ABC,BCD,CDA,GEF,EGH,GHF,HFE BAD,ABC,BCD,CDA,GEF,EGH,GHF,HFE

The lines that form angle BAD are: BA+AD

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 GEF are: GE+EF

The lines that form angle EGH are: EG+GH

The lines that form angle GHF are: GH+HF

The lines that form angle HFE are: HF+FE

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

Answer

8