Shape
Copyright David & Cynthia Thomas, 2009
Necessary Conditions--Exercises
Part I
Do challenge problem and directed activities in this section.
Part II
Complete the following exercises
1. Given the following components, state whether a triangle may be constructed.
a. Three segments of length
i. 5, 9, 3
ii. 17, 1, 17
b. Three angles
i. 45°, 45°, 45°
ii. 100°, 79°, 1°
2. Create three triangles using straightedge-and-compass. Using a protractor and metric ruler, measure their respective segments and angles and confirm that the Triangle Inequality Theorem and Triangle Angle Sum Theorem are both true for each triangle.
3. A link to Proposition 1 of Euclid’s Elements is found I the directed activity Construct an Equilateral Triangle Using Straightedge-and-Compass. Study the proof carefully then rewrite it in your own words, explaining why the construction “works”.
4. Create a Concept Card for the Triangle Inequality Theorem
5. Create a Concept Card for the Triangle Angle Sum Theorem
6. Create a Concept Card for Equilateral Triangles