Common Core: 8th Grade Math

Explore the foundational concepts of mathematics, including algebra, geometry, and data analysis, essential for 8th-grade students.

Linear Equations and FunctionsThe Pythagorean TheoremData Analysis and Statistics
Systems of Linear EquationsVolume of Cylinders, Cones, and SpheresTransformations and Congruence
Budgeting and Money MathMath in Sports and GamesEngineering and Design
Breaking Down Word ProblemsChecking Your Work
Linear Equations and...The Pythagorean Theo...Data Analysis and St...Systems of Linear Eq...Volume of Cylinders,...Transformations and ...Budgeting and Money ...Math in Sports and G...Engineering and Desi...Breaking Down Word P...Checking Your Work
Advanced Topics

Transformations and Congruence

Moving and Matching Shapes

Transformation means changing a shape's position, size, or orientation. In 8th grade, you'll learn about translations (slides), rotations (turns), reflections (flips), and dilations (resizing).

Types of Transformations

  • Translation: Slide the shape up, down, or sideways.
  • Rotation: Turn the shape around a point.
  • Reflection: Flip the shape over a line.
  • Dilation: Make the shape bigger or smaller but keep its proportions.

If two shapes match exactly after a transformation (except for dilations), they are congruent.

Why It Matters

Understanding transformations helps in art, design, and even robotics, where you need to predict how objects move and fit together.

Examples

  • A triangle flipped over the x-axis is a reflection.

  • A logo resized to fit a t-shirt uses dilation.

In a Nutshell

Transformations show how shapes move or change, and congruence shows when shapes are exactly alike.

Key Terms

Transformation
A change in a shape's position, size, or orientation.
Congruent
Shapes that are exactly the same size and shape.
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Budgeting and Money Math