S9
Symmetry & Transformation
Reflection → Group
"If it looks the same after a change, that is symmetry."
Philosophical Origin：Galois theory
Minimal Example
Square has 4 rotations and 4 reflections, total 8 symmetries.
One-Line Rule
"Symmetry is invariance under transformation."
Common Misconception vs Correct Understanding
Symmetry is just mirror image.
Symmetry includes rotation, reflection, translation.
🌱 Growth Steps (Natural Evolution)
1 / 5 步
1
Reflection: Mirror symmetry
✨ Starting Point: Growth begins here
如果你能 ↑ 那么你就能 ↓
2
Rotation: Turn symmetry
如果你能 ↑ 那么你就能 ↓
3
Translation: Shift symmetry
如果你能 ↑ 那么你就能 ↓
4
Composition: Combine transformations
如果你能 ↑ 那么你就能 ↓
5
Group theory: Abstract symmetry
SAT Example Question
Question:
How many lines of symmetry does a regular hexagon have?
Answer:
6
Explanation:
3 through opposite vertices + 3 through midpoints
Practice Questions
5 questions with multiple solution methods
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