Rigid Transformations in Geometry

What is the primary characteristic of a rigid transformation?

Which of the following transformations involves moving a figure without changing its orientation?

What type of transformation is described as flipping a figure over a line?

In a rotation, what remains constant about a point on the figure?

Which transformation involves changing the position of a triangle 3 units to the right and 2 units up?

Rigid Transformations

Rigid transformations preserve the shape and size of figures, preventing distortion.
Distances between points and angles remain unchanged during rigid transformations.

Types of Rigid Transformations

Translation
- Moves every point of a figure the same distance in a specific direction.
- The shape and orientation of the figure remain constant; only the position changes.
- Example: Translating a triangle 3 units right and 2 units up shifts all points equally.
Rotation
- Rotates a figure around a fixed point, known as the center of rotation, by a specified angle.
- Distances from the center of rotation to all points on the figure remain the same.
- Example: A square rotated 90° clockwise around its center maintains congruency to its original position.
Reflection
- Flips a figure over a line, referred to as the line of reflection.
- Creates a mirror image of the figure, with each point having a corresponding point on the opposite side of the line.
- Example: Reflecting a pentagon over the y-axis results in each point moving to an equal distance on the opposite side of the axis.

This quiz focuses on the concept of rigid transformations in geometry, including translation, rotation, and reflection. It explores how these transformations preserve the shape and size of figures, ensuring that distances and angles remain unchanged. Test your understanding of these crucial geometric principles.