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12.7: Chapter 12 Review

Difficulty Level: At Grade Created by: CK-12
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Keywords & Theorems

Exploring Symmetry

  • Line of Symmetry
  • Line Symmetry
  • Rotational Symmetry
  • Center of Rotation
  • Angle of Rotation


  • Transformation
  • Rigid Transformation
  • Translation


  • Reflection
  • Line of Reflection
  • Reflection over the \begin{align*}y-\end{align*}axis
  • Reflection over the \begin{align*}x-\end{align*}axis
  • Reflection over \begin{align*}y = x\end{align*}
  • Reflection over \begin{align*}y = -x\end{align*}


  • Rotation
  • Center of Rotation
  • Angle of Rotation
  • Rotation of \begin{align*}180^\circ\end{align*}
  • Rotation of \begin{align*}90^\circ\end{align*}
  • Rotation of \begin{align*}270^\circ\end{align*}

Compositions of Transformations

  • Composition (of transformations)
  • Glide Reflection
  • Reflections over Parallel Lines Theorem
  • Reflection over the Axes Theorem
  • Reflection over Intersecting Lines Theorem

Extension: Tessellating Polygons

  • Tessellation

Review Questions

Match the description with its rule.

  1. Reflection over the \begin{align*}y-\end{align*}axis - A. \begin{align*}(y, -x)\end{align*}
  2. Reflection over the \begin{align*}x-\end{align*}axis - B. \begin{align*}(-y, -x)\end{align*}
  3. Reflection over \begin{align*}y = x\end{align*} - C. \begin{align*}(-x, y)\end{align*}
  4. Reflection over \begin{align*}y = -x\end{align*} - D. \begin{align*}(-y, x)\end{align*}
  5. Rotation of \begin{align*}180^\circ\end{align*} - E. \begin{align*}(x, -y)\end{align*}
  6. Rotation of \begin{align*}90^\circ\end{align*} - F. \begin{align*}(y, x)\end{align*}
  7. Rotation of \begin{align*}270^\circ\end{align*} - G. \begin{align*}(x, y)\end{align*}
  8. Rotation of \begin{align*}360^\circ\end{align*} - H. \begin{align*}(-x, -y)\end{align*}

Texas Instruments Resources

In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9697.

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