Cutting Squares
Paired Activity 1 from OMO 2011
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Each of the problems in this activity require you to show how to cut a figure and then rearrange the pieces to form another figure of figures.  You should draw lines indicating where you would cut each figure, and also draw the resulting figure with lines showing the outline of each piece.
1. Cut a 7 × 7 square into a 4 × 4 square, a 3 × 3 square and 4 congruent right angled triangles.  Draw the result.
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2. Cut the given square and rearrange the pieces into 2 congruent squares.  Draw the result.
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3. Transform the given square into an equilateral triangle and label the proper vertex of each of the corners of each piece in the equilateral triangle.  Draw the result.
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4. a) Cut a 1 × 5 rectangle into 5 pieces that can be rearranged to form a square.  Draw the result.
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4. b) Cut a 1 × 5 rectangle into 4 pieces that can be rearranged to form a square.  Draw the result.
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5. Cut a square and rearrange the pieces into 5 congruent squares.  Draw the result.
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6. Cut a square and rearrange the pieces into 2 non-congruent squares.  Draw the result.
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7. Cut the square C into 6 pieces so that they can be arranged to form squares A and B.  Draw the result.
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