The washing line

Three squares and three common vertices. Prove that the quadrilateral ABCD is a rectangle.

Scroll down for a solution to this problem.


Solution by kasumi020.

Look at the two triangles FEB and AED. The angles at vertex E are easily seen to be congruent, as are the adjacent sides. From SAS we conclude these triangles are congruent.

So AD has the same length as square side FB. It must therefore be parallel to BC, and so ABCD is a rectangle.

Visual solution

Proof without words by David Andriana.


Tooth bridges and toothpaste
soap, soap box
and the washing line
All together with pegs to dry
The wind is strongly blowing
With an eerie atmosphere feeling
Socks, shirts and dresses are hanging
The sun comes out, the clouds are racing
Washing lines have much for saying


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