Lesson Plan: Lesson plans were written by Maryland mathematics educators and could be used when teaching the concepts.
 Goal 2 Geometry, Measurement, And Reasoning Expectation 2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate. Indicator 2.1.3 The student will use transformations to move figures, create designs, and/or demonstrate geometric properties.

### Lesson Content

Line Symmetry and Reflections

### Objective

The student will be able to identify similarities and differences between the images and pre-images generated by reflections, apply reflections to determine the coordinates of figures, and apply reflections to real-world situations.

45-minute lesson

### Essential Questions

What are the similarities and differences between the images and pre-images generated by reflections?

What is the relationship between the coordinates of the vertices of a figure and the coordinates of the vertices of the figure's image generated by reflections?

How can reflections be applied to real-world situations?

### Warm-Up/Opening Activity

Investigate reflectional symmetry.

Worksheet: Line Symmetry

### Development of Ideas

Activity:

Investigate and apply reflections using a Mira™ and patty paper.

Worksheet: Reflections

Optional Activity

Investigate and draw reflections on a coordinate plane.

Worksheet (Cabri): Reflections on a Coordinate Plane

### Closure

Summary questions

Compare translations and reflections. What is the same? What is different?

Answer: The size and the shape of the pre-image and image are the same (because they are isometries) but the orientation is different in reflections compared to translations (pre-image and image have the same orientation).

Janet constructed the perpendicular from each of the vertices of a triangle to a line. How will this help her to find the image of the triangle reflected over the line?

Answer: Since Janet has constructed the perpendicular to a line from each vertex, she can use each constructed line to help create a reflection. Janet can measure the distance from each vertex to the line, copy that distance to the other side of the line and mark a new vertex. This new vertex will be the reflection of the original vertex. Repeating this for each vertex and connecting the vertices, Janet will complete a reflection of the original triangle.