8th Grade Math

Algebra foundations, geometry, and mathematical modeling for eighth grade students.

Advanced Topics

Transformations and Congruence

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.

In a Nutshell

Transformations change a shape's position or size; congruence means shapes are identical.