Задача Задача №3745812
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Assuming the shapes are regular (all sides and angles equal):
Quick answers
- Folds in half (lines of symmetry): pentagon 5, hexagon 6, octagon 8.
- Turns that fit exactly: pentagon 5, hexagon 6, octagon 8.
- Equilateral triangle: 3 folds, 3 turns.
- a 108°
b 120°
c 135° - For a regular polygon, lines of symmetry = order of rotational symmetry = number of sides.
- 20
Why
- A regular shape can be turned by \(360° \div n\) and still look the same. It also has \(n\) symmetry lines.
- Angle formula: \[ \text{each angle}=\frac{(n-2)\times180°}{n} \]
- Pentagon: \(3\times180=540\), \(540\div5=108°\)
- Hexagon: \(720\div6=120°\)
- Octagon: \(1080\div8=135°\)
Check: both symmetry counts match the number of sides.
Обсуждение
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5 and 6
5. For a regular polygon:
- number of sides = number of mirror lines
- number of sides = number of same-looking turns
Example: a square has 4 sides, 4 mirror lines, and 4 turns.
6. 20
If a regular shape has 20 mirror lines, it has 20 sides.
It also has 20 turns that look the same.
Each turn is \(360^\circ \div 20 = 18^\circ\).
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