Three congruent right triangles. What fraction is shaded?

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## Solution

The shaded fraction is 1/3.

From congruence we know that ∠EAB equals ∠DBC. Therefore line segments EA and BC are parallel. Now we can shear vertex C of triangle AEC along CB to B. The shaded fraction then coincides with triangle AEB, which is one third of the total.

## Poem

The sailing boat

Is setting of

To raise and sail in the wind

Chasing the waves

And floating alone

Under the sweet sky smiles

Winds so nice blow and blow

The boat curls on the water

Between the foam and salted pearls

The boat is going it’s own way

Towards the mysteries anyway