Lab 5

This lab has several parts. Be sure to allot your time so that you work with each part.

A. Parallel strips as a locus

Download this Sketchpad file and work through it.

What you will find:

• Trace a disk along a segment or a line to get a sausage or a strip.
• Construct a strip using parallel lines
• Intersect strips for two intersecting lines
• Intersect strips for three extended sides of a triangle.
• Relationship to angle bisectors, incircles and excircles

B. Dilations

Download this Dilation Example File

• See examples and a graph. Compare change in area or length with dilation ratio.
• Finding a dilation center

Common Tangents: An important construction (download GSP file)

• Application to common tangents of circles

C. Shears

Download this Shear Investigation File

• Given points A, B, C, D there is a shear that leaves points of line AB fixed and moves line AC to line AD (We do NOT assume C shears to D. C and D just control the lines.)
  • We make (and provide) a tool for this.
• What happens to areas when figures are sheared?
• What happens to the shape of a circle or a square?