# GeoGebra

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## Triangle Paradox (Missing square puzzle)

The two shapes have the same area. So where's the black square come from then?
5

Shared by Michael Borcherds

Material Type
Worksheet
Tags
missing  paradox  disappearing  area  triangle  square  puzzle
Target group (age)
11-14
Language
English (US)

GeoGebra version
4.0
Views
20586
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Derived Materials
Shared by Edward

## Write a comment

• Hi,
can somebody help with this triangle paradox
I do not understand how the difference is there.
Normally the surface should be 52? = 104/2
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• It's very simple Solving
These two triangles are’nt congruent. The triangle shown in the figure, wich square is equal 51.5 is less than a second triangle with a small triangle painted yellow (on my figure). His field is 1. Exactly: green triangle had a vertex in the grid point, and now this point does not belong to the second triangle of 51.5. This triangle should extend to the quadrilateral.

Bronek Pabich – Poland
www.pabich.interklasa.pl
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• The question is to realize that when you swap the green and purple triangles, the slope isn't the same because both triangles aren't proportional. So the whole figure is not a triangle... is a quadrilateral. I thing is what Pabich said (I don't understand him very well).
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• I think "similar" is better than "propotional". Also, Wikipedia stated that too.
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• This should be renamed to "Missing Square Puzzle" per Wikipedia
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