Exercises (Page 224)
1. In each of the following figures, a hole was punched in a folded square sheet of paper and then the paper was unfolded. Identify the line along which the paper was folded.
The positions of the holes tell us where the fold line (line of symmetry) must be. The fold line is always exactly halfway between the two matching holes.
- (a) Holes are side-by-side horizontally. Fold: Vertical line.
- (b) Holes are at diagonal corners. Fold: Diagonal line.
- (c) Holes are stacked vertically. Fold: Horizontal line.
- (d) Only one hole is visible, but the question implies unfolding. If the figure creates 4 holes from one punch, it was folded twice (vertically then horizontally). If it implies a single fold for a single hole, the question asks “How was it folded?” - For figure (d) in the solution key, it indicates folds vertically and horizontally to create the pattern shown in answers.
2. Given the line(s) of symmetry, find the other hole(s):
We need to “reflect” the existing hole across the dotted line.
3 & 4. Paper Cutting Predictions
(a) Vertical fold, cut a triangle pointing right.
- Result: When opened, you get a diamond or rhombus shape in the center.
(b) Horizontal fold, cut a pattern on the edge.
- Result: The pattern mirrors on the top and bottom.