Transformations

Ever notice how some shapes look exactly the same, just in different positions? These are congruent figures - they have identical size and shape with matching side lengths and angles.

There are three main types of rigid transformations that move shapes without changing their size or shape. A translation slides a shape in a straight line - like moving triangle ABC to position DEF while keeping it facing the same direction. A rotation turns a shape around a point - imagine spinning triangle ABC until it lines up with triangle EGF. A reflection flips a shape across a line - creating a mirror image, just like triangle ABC and triangle DEF reflecting across an invisible mirror line.

Unlike the rigid transformations, a dilation creates a larger or smaller version of a shape. When one shape is a scaled version of another, we call them similar figures rather than congruent. Think of it like zooming in or out on a photo - the proportions stay the same, but the size changes.

Real-world connection: Transformations are everywhere! Video game designers use translations to move characters across the screen, architects use rotations to position buildings for optimal sunlight, and reflections create symmetry in art and design.