Shape 

Copyright David & Cynthia Thomas, 2009

Triangle Recipes--Exercises

Part I

Do challenge problem and directed activities in this section.

Part II

Complete the following exercises

1. Using either straightedge-and-compass or The Geometers Sketchpad, construct triangles with the following features:

a. Segments of length 6cm, 8cm, and 10cm

b. Segments of length 8cm, 8cm, and 10cm

c. Segments of length 6cm and 8cm and an included angle of 45°.

d. Segments of length 6cm and 10cm and an included angle of 60°.

2. Which construction strategy is more precise: Straightedge-and-compass, The Geometers Sketchpad, or paper folding? Why? 

3. An isosceles triangle has exactly two sides of the same length.  Construct an isosceles triangle using straightedge-and-compass, The Geometers Sketchpad, and paper folding.  Explain why each construction “works”. 

4. A link to Proposition 8 of Euclid’s Elements is found in directed activity Duplicate a segment of unknown length.  Study the proof carefully then rewrite it in your own words.

5. A link to Proposition 4 of Euclid’s Elements is found in directed activity Side-Side-Side.  Study the proof carefully then rewrite it in your own words.

6. Explain why the construction described in Table 1.4 “works”.

7. Explain why the construction described in Table 1.5 “works”.

8. Create a Concept Card for Side-Side-Side

9. Create a Concept Card for Side-Angle-Side