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

 

 logo.jpg