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

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## Solution

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

## Poem

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