Counting Perpendicular Lines: Analysis of Nested Square Geometry

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

AAABBBCCCDDDEEEFFFGGGHHH

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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

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1

Understand the problem

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

AAABBBCCCDDDEEEFFFGGGHHH

2

Step-by-step solution

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 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.

3

Final Answer

8

Practice Quiz

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What do the four figures below have in common?

1234

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