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## Folding to pyramid

A square and an equilateral triangle. The square is folded as shown. What is the angle α?

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## Folding a pentagon

One side of a regular pentagon is folded back and forth as shown. Are the six red line segments congruent?

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## Folding magic

One corner of a rectangular piece of paper is folded as shown. Prove that the red line segments are concurrent.

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## Folded napkin II

A unit square paper is folded as shown. What is the red area?

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## The secret document

One corner of a rectangular piece of paper is folded back and forth to the opposite side. What is the proportion red : blue?

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## The sneak peek

A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?

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## Take five origami

Divide a rectangular piece of paper in five pieces of equal area. You only have a pair of scissors at your disposal, but you are allowed to make straight folds to guide you.

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## The kingsize bed

A rectangle with an inscribed right triangle. What is ac/bd?

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## The folded napkin

A square sheet of paper is folded symmetrically from a corner. If the fold length is 4, what is the area of the triangle formed by the other three corners?

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## The bobline

A regular hexagon is folded back and forth along the dotted line. What fraction of the area is yellow?