Counting Perpendicular Lines: Finding All Line Pairs in a Square

How many pairs of perpendicular lines are there in the square below?

AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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
00:13 Let's mark and count all the right angles
00:19 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

How many pairs of perpendicular lines are there in the square below?

AAABBBCCCDDD

2

Step-by-step solution

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

Our right angles are:

ABC,BCD,CDA,DAB ABC,BCD,CDA,DAB

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

Since in a rectangle we have 4 marked angles of 90 degrees, we must have 4 pairs of perpendicular lines.

3

Final Answer

4

Practice Quiz

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What do the four figures below have in common?

1234

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