| The Investigation poses questions to generate interest in various mathematical topics from the text and encourages students to formulate and investigate their own conjectures. One use of the investigations is for term papers in which students report on their conjectures and the patterns they find.
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 Read Me - Laboratory Investigation
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Laboratory Investigation 11.1Paper Folding
This investigation can be carried out by drawing a triangle on a sheet of paper and then folding the paper, or using a Mira, or using a straightedge and compass for the constructions. Or, the constructions can be performed with computer software programs. Regardless of which method is used, one triangle should be drawn and used for all three constructions in 1 through 3. To provide the most general results, use a triangle that is scalene and not a right triangle.  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072532947/78543/LI_11_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (15.0K)</a>]]>- Construct the perpendicular bisectors of the three sides of the triangle. What conjecture can you make about these three lines? Test your conjecture by sketching some other triangles to see if it is true.
- Construct the line passing through each vertex and the midpoint of the opposite side of a triangle. What conjecture can you make about these three lines?
- Construct the bisectors of the three angles of a triangle. Form a conjecture about these three lines. Test your conjecture by sketching some other triangles.
- There is a relationship among the three types of constructions in 1 through 3. What is this relationship? (Hint: It may help to combine the information from these three types of constructions onto one copy of the triangle.)
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