Dissections and Proof Part A: Tangrams (15 minutes)

One set of tangram pieces can make more than one shape. Geometric language helps you give clear descriptions of how to move pieces to change one shape into another. Roll your cursor over each of the three images below to see an animation of that move.

Slide or Translation
Here, a parallelogram made of two small triangles becomes a square as you slide one of the small triangles parallel to the base of the parallelogram. This type of movement is known as a translation. Try this with your tangram pieces.

Flip or Reflection
Here, the parallelogram becomes a triangle when you flip one of its halves (small triangles) at its horizontal midline. This type of movement is called a reflection. Try it.

Rotation
Here, a square becomes a triangle when you rotate one of its two halves (small triangles) 270° around vertex A. This type of movement is called a rotation. Try it.

Problem A3
For each of the pairs of figures below, do the following:

• Build the shape on the left with your tangram set.
• Turn it into the shape on the right by reflecting, rotating, or translating one of two of the pieces. (This may take more than one step.)
• Write a description, telling which piece or pieces you moved and how you moved them.

a. b. c.

Problem A3 adapted from Connected Geometry, developed by Educational Development Center, Inc. pp. 162-163. © 2000 Glencoe/McGraw-Hill. Used with permission. www.glencoe.com/sec/math

Problem A1

Problem A2

Here is one possible solution:

Problem A3