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Problem of the Week
Problem A
Paper Folding

Start with a square piece of paper, and label the corners \(A\), \(B\), \(C\), and \(D\), starting with the top-left corner and moving clockwise.

  1. Fold the paper so that corner \(A\) touches corner \(C\). What shape did you make?

  2. Open the paper up so that you are back to the square, but with a diagonal crease. Fold the paper so that the edge between corners \(A\) and \(B\) lines up with the diagonal crease. Then fold the paper so that the edge between corners \(C\) and \(D\) lines up with the diagonal crease. What shape did you make?

  3. Open the paper up so that you are back to the square. Fold the paper so that corner \(D\) touches corner \(A\) and corner \(C\) touches corner \(B\). What shape did you make?

  4. Continuing from the shape you made in part (c), fold the paper so that corners \(B\) and \(C\) touch the fold line. What shape did you make?

  5. Fill in the Venn diagram below with the letters \(a\), \(b\), \(c\), and \(d\), representing the shape you made in each part.

    A Venn diagram with 3 overlapping circles. One of the circles is labelled has 4 sides, one is labelled has a right angle, one is labelled has half the area of the original square.

Theme: Geometry & Measurement