Exercises (Page 226)
5. Suppose you have to get each of these shapes with some folds and a single straight cut. How will you do it?
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a. The hole in the centre is a square.
- Strategy: Fold the paper vertically, then horizontally (quarter fold).
- Cut: Cut the corner that corresponds to the center of the paper. Since the desired shape is a square (straight edges), you cut diagonally across that corner if the square is tilted, or cut a square notch if it’s aligned.
- Correct Method: Fold vertically, then horizontally. At the closed corner (center), cut off a small isosceles right triangle. When unfolded, the 4 triangles form a square (diamond orientation).
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b. The hole in the centre is a square (aligned).
- Strategy: Fold vertically, then horizontally.
- Cut: Cut a square notch at the closed corner.
6. How many lines of symmetry do these shapes have?
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(a) Square diamond shape with extensions:
- Looking at the figure, it has symmetry along the vertical, horizontal, and both diagonal axes.
- Answer: 4 Lines of Symmetry.
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(b) A triangle with equal sides and equal angles (Equilateral Triangle):
- Answer: 3 Lines of Symmetry.
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(c) A hexagon with equal sides and equal angles (Regular Hexagon):
- Answer: 6 Lines of Symmetry.
7. Trace each figure and draw the lines of symmetry, if any: