Advanced Topics
In a nutshell: Transformations change a shape's position or size; congruence means shapes are identical.
## Moving and Matching Shapes
**Transformations** are ways to change a shape's position or size while keeping its properties. The main types are:
- **Translation**: Sliding a shape without turning it.
- **Reflection**: Flipping a shape over a line.
- **Rotation**: Turning a shape around a point.
- **Dilation**: Making a shape larger or smaller.
**Congruence** means two shapes are exactly the same size and shape, even if they are in different positions.
### Visualizing Transformations
Using graph paper helps to see how a shape moves or changes. Transformations are used in design, games, and art.
#### Quick Tips
- Use tracing paper to check if shapes are congruent.
- Remember: congruent shapes can be rotated or flipped and still match.
Examples
- Slide a triangle three units right and two units up.
- Reflect a letter 'A' over the y-axis to see its mirror image.