Finding Perpendicular Line Pairs: Cross-Shaped Geometric Analysis

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

AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLL

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Step-by-step video solution

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00:04 How many perpendicular lines can you find in this drawing?
00:09 Remember! A perpendicular line forms a right angle where it meets another line.
00:16 Let's carefully mark and count each right angle together. Take your time.
00:32 Great work! That's how we solve this problem.

Step-by-step written solution

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1

Understand the problem

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

AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLL

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,CDE,DEF,EFG,FGH,GHI,HIJ,IJK,JKL,KLA,LAB ABC,BCD,CDE,DEF,EFG,FGH,GHI,HIJ,IJK,JKL,KLA,LAB

The lines that form angle ABC are: AB+BC

The lines that form angle BCD are: BC+CD

The lines that form angle CDE are: CD+DE

The lines that form angle DEF are: DE+EF

The lines that form angle EFG are: EF+FG

The lines that form angle FGH are: FG+GH

The lines that form angle GHI are: GH+HI

The lines that form angle HIJ are: HI+IJ

The lines that form angle IJK are: IJ+JK

The lines that form angle JKL are: JK+KL

The lines that form angle KLA are: KL+LA

The lines that form angle LAB are: LA+AB

Due to the fact that in the drawing we have 12 angles of 90 degrees marked, we must have 12 pairs of perpendicular lines.

3

Final Answer

12

Practice Quiz

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What do the four figures below have in common?

1234

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