Parallel and Perpendicular lines in Paper Folding

Transcript

Parallel and Perpendicular lines in Paper Folding We can fold the paper horizontally to make parallel and perdicular lines Answers to some questions in the book are How would you describe the opposite edges of the sheet? They are __________ to each other. They are parallel to each other. Opposite edges of a square maintain a constant distance and will never intersect. How would you describe the adjacent edges of the sheet? The adjacent edges are __________ to each other. The adjacent edges are perpendicular to each other. They meet at the corners to form right angles (90°). Fold the sheet horizontally in half... How many parallel lines do you see now? How does the new line segment relate to the vertical sides? You now see three parallel lines: the top edge, the bottom edge, and the new crease in the middle. The new horizontal line segment is perpendicular to the vertical sides. Make one more horizontal fold in the folded sheet. How many parallel lines do you see now? After making one more horizontal fold and then unfolding the sheet, you will see five parallel lines (the two original edges and three creases). What will happen if you do it once more? How many parallel lines will you get? Is there a pattern? If you do it once more (a third fold), you will get nine parallel lines. Yes, there is a pattern: if n is the number of folds, the number of parallel lines is 2n + 1. This pattern will continue with more folds. Make a vertical fold in the square sheet. This new vertical line is __________ to the previous horizontal lines. This new vertical line is perpendicular to the previous horizontal lines, as it will intersect them at right angles. Fold the sheet along a diagonal. Can you find a fold that creates a line parallel to the diagonal line? Yes. One way to do this is to take one of the corners that the diagonal does not pass through and fold it over to touch the diagonal line. The new crease you make will be parallel to the original diagonal.