Symmetry and Transformations
What is Symmetry?
Symmetry is when a shape or picture looks the same even after you move it in a certain way. It's like having a matching pattern on both sides!
Line Symmetry
Line symmetry (or reflection symmetry) happens when you can fold a shape along a line, and both halves match exactly. This line is called a line of symmetry.
Examples of things with line symmetry:
- The letter A has a vertical line of symmetry down the middle
- A butterfly's wings show line symmetry
- Your face has approximate line symmetry
Some shapes have more than one line of symmetry:
- A rectangle has 2 lines of symmetry
- A square has 4 lines of symmetry
- A circle has infinite lines of symmetry
Rotational Symmetry
Rotational symmetry happens when a shape looks the same after you turn (rotate) it around a center point. If you can rotate a shape less than a full turn and it looks the same, it has rotational symmetry.
Examples of things with rotational symmetry:
- A square has rotational symmetry - it looks the same after turning it 90°, 180°, 270°, or 360°
- The letter S has rotational symmetry - it looks the same after turning it 180°
- A pinwheel has rotational symmetry
What are Transformations?
Transformations are ways to move shapes without changing their size or shape. There are three main types:
1. Translations (Slides)
A translation moves a shape by sliding it in any direction without turning it. It's like sliding a book across a table.