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A Second Challenge

Cindy Oliver
7th grade
Ola Middle School
Henry County Schools

Contents

Task
Overview
In this task, students will construct a reflection of a triangle over a given line of symmetry. The students will also be able to create the line of symmetry using the reflected triangle.

Illustrative Task
In the drawing below, line l is perpendicular to line m. You can check this by folding the paper along line m and seeing that line l reflects upon itself. Can you construct a reflection of △ABC using only Euclidean tools and line m as a line of reflection? Label the corresponding point for vertex A as A’, B as B’, and C as C’.

  1. Discuss exactly how you constructed the reflection and how you know it is a reflection. You might find it helpful to label the vertices of the reflected triangle and to use the following notations in your writing:
    • means the distance from point A to point P
    • means the line segment from point A to point P
    • △ABC means the triangle with vertices A, B and C
    • ∠A means the angle that has a vertex of A
  2. On your next construction, if you place the point of your compass on the line of reflection and the pencil of the compass on any vertex and construct a circle, the circle should pass through another point you have constructed.
  3. Two geometric objects are congruent if you can reflect one onto another. Verify that your constructed reflection of △ABC is congruent to △ABC by folding your paper along line m.
  4. Place your compass at point A and construct a circle that has a radius greater than the distance from A to P. Without changing the width, place the point of the compass at the point that is the reflection of point A and construct another circle.

GPS Addressed
M7G2. Students will demonstrate understanding of transformations.
  1. Demonstrate understanding of translations, dilations, rotations, reflections and relate symmetry to appropriate transformations.

Video Information
Use these questions to guide your thinking about some of the important teacher ideas in the lesson featured in the video clip.
  1. What kinds of questions does the teacher ask to promote students’ problem solving?
  2. How is the teacher gauging students’ current understandings and building from those understandings?
  3. Consider the GPS standards listed with this video.
  4. What makes this lesson different from lessons you have taught on this topic?

Classroom Materials

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