Which transformation preserves congruence?

A **congruence transformation** is a type of transformation that preserves the shape and size of a figure, meaning that the figure and its image are congruent. The main types of congruence transformations are:

1. **Translation:** Slides a figure from one position to another without rotating or flipping it. The size and shape of the figure remain unchanged.
  
2. **Rotation:** Turns a figure around a fixed point (the center of rotation) through a specific angle. The figure's shape and size stay the same.
  
3. **Reflection:** Flips a figure over a line (the line of reflection) to create a mirror image. The figure's shape and size remain identical, though its orientation changes.
  
4. **Glide Reflection:** A combination of a translation followed by a reflection across a line parallel to the direction of the translation. It also preserves congruence.

All these transformations maintain congruence because they do not alter the lengths of sides or the measures of angles in the figure.

Would you like more details or have any questions?

Here are five related questions:

1. How does a rotation differ from a translation in terms of the final position of a figure?
2. What is the effect of a reflection on the orientation of a figure?
3. Can a glide reflection result in the same figure as a simple reflection or translation?
4. How can you determine the angle of rotation required to map a figure onto itself?
5. What are examples of real-world situations where congruence transformations are used?

**Tip:** To check if two figures are congruent after a transformation, compare their corresponding sides and angles; they should be exactly equal in length and measure.

Explore how congruence transformations such as translation, rotation, reflection, and glide reflection preserve the shape and size of figures in geometry. Learn their definitions and applications with examples. Suitable for Grades 6-8 students.

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