Geometry: Transformations: Reflections

Objectives

• Students will identify a reflection as an isometry, also called a congruence transformation.
• Students will identify which properties are preserved in a reflection and which are not.
• Students will identify coordinates of an image that is reflected over the x-axis, the y-axis, and both axes.
• Students will generalize the relationship between the coordinates of a point and the coordinates of its reflection in the coordinate plane.

Vocabulary

• Pre-image
• Image
• Transformation
• Reflection
• Congruent figures
• Congruence transformation
• Isometry

About the Lesson

Model reflections and identify the properties that are preserved in a reflection and those that are not. Then they will identify and generalize the coordinates of a triangle under reflections over the axes in the coordinate plane. As a result, students will:

• Reflect a triangle over a line and over the axes in the coordinate plane to develop their visualization and spatial sense of a reflection.
• Describe the consequences of the reflection in terms of identifying those properties which are preserved and those which are not, and identify and generalize the coordinates of reflections in the coordinate plane.
• Infer that a reflection does not alter any of the measurements of a reflected object, and as such, a reflection is an example of an isometry, or congruence transformation.