Math 487 Lab 2

Materials needed

  1. GTC: Geometry Through the Circle, pp. 57-64. (This book is available in the University Book Store.
  2. Plan a way to store your files. Either bring a disk or plan to transfer your files to your Dante account.

This Material is on the Web but can be printed out

  1. The second part of this lab is Lab 2 Part B.
  2. OPTIONAL. Part B contains an introduction to the longer pdf file, GASP 4. Introduction to Line Reflection. The GASP document is available as a resource and a supplement (and it has figures), but the essential part of the Lab is on the Lab 2 Part B web page.

Lab Activity

Part A. Inscribed Circles and Symmetry.

We constructed some circles tangent to a line in class earlier in the week. The goal here is to see one way to understand circles inscribed in an angle through seeing the angle bisector as a line of symmetry. To do this, you will use Line Reflection in Sketchpad.

How to Reflect an Object across a line m in Sketchpad. First, we Mark m as the Mirror. To do this, select m and choose Transform > Mark Mirror. Then Select the object or objects to be reflected and choose Transform > Reflect. The mirror m stays marked until a new mirror is marked, so you can reflect additional objects across the same mirror by selecting them and choosing Transform > Reflect.

  1. GTC, page 57, Exp 5.1, Inv 1. Skip p. 58.
  2. GTC, page 59, Exp 5.2, Inv 1. Skip p. 60.
  3. Skip GTC, Exp 5.1, Inv 2 but note that we did this in class.
  4. GTC, pp. 62-64, Exp 5.1, Inv 3. Skip the Explore More on p. 64
  5. Draw an angle ABC and construct the angle bisector.Given a point E on the angle bisector, construct a circle with center E that is tangent to both rays BA and BC.
  6. Draw an angle ABC. Given a point F on ray BA, construct a circle through F that is tangent to both rays BA and BC.

Part B. Line Reflections and Kaleidoscopes

  1. Follow this link for Lab 2, part B.