1.01 - Construction Basics

Mr. Braddock

<section class="section2"><h2>Objective(s)</h2> <ul> <li>Create diagrams using a straightedge</li> <li>Use a compass to construct a circle</li> </ul> <p>Required materials: compass, straightedge, patty paper</p> <hr/> </section><section class="section2"><h2>Warm Up</h2> <p>Gain familiarity with the construction tools by drawing multiple lines and circles. Then, follow these steps:</p> <ul> <li>Draw a point, label it <script type="math/tex">A</script> </li> <li>Draw a circle centered at <script type="math/tex">A</script> </li> <li>Mark a point on the circle, label it <script type="math/tex">B</script> </li> <li>Draw a circle centered at <script type="math/tex">B</script> going through <script type="math/tex">A</script> </li> <li>Draw segment <script type="math/tex">\overline{AB}</script> </li> </ul> <hr/> <section class="section3"><h3>Definitions</h3> <p><strong>Line segment</strong>: a set of points on a line with two endpoints</p> <div class="fragment"> <p><strong>Circle</strong>: a set of all points that are the same distance (radius) from a given point (center)</p> </div><hr/> </section></section><section class="section2"><h2>Illegal Moves</h2> <p>Given segment <script type="math/tex">\overline{AB}</script>, follow these steps:</p> <ul> <li>Draw a circle centered at <script type="math/tex">A</script> with radius <script type="math/tex">AB</script> </li> <li>Mark a point at the middle of <script type="math/tex">\overline{AB}</script>, label it <script type="math/tex">C</script> </li> <li>Draw a circle centered at <script type="math/tex">B</script> with radius <script type="math/tex">BC</script> </li> <li>Label the intersection above <script type="math/tex">B</script> as <script type="math/tex">D</script> and below <script type="math/tex">B</script> as <script type="math/tex">E</script> </li> <li>Draw segments <script type="math/tex">\overline{AD}</script>, <script type="math/tex">\overline{DE}</script>, and <script type="math/tex">\overline{AE}</script>, and trace <script type="math/tex">\Delta ADE</script> onto patty paper</li> </ul> <hr/> <section class="section3"><h3>Discussion</h3> <p>Compare your <script type="math/tex">\Delta ADE</script> with your neighbors.</p> <p>Why might they be different? How could we ensure they are all the same?</p> <hr/> </section><section class="section3"><h3>Valid Construction Moves</h3> <ul> <li>Draw points in blank space, on objects, and at intersections</li> <li>Draw segments, rays, and lines through two points</li> <li>Draw a circle centered at a point and through another point</li> <li>Set compass to a length between two points then move the compass</li> </ul> <hr/> </section></section><section class="section2"><h2>Perfect Copy</h2> <p>The figure shows the first few steps of constructing a regular hexagon. Complete the construction.</p> <p>(image)</p> <hr/> <section class="section3"><h3>Reflection</h3> <p>How does your regular hexagon compare to your neighbors?</p> <p>A <strong>regular polygon</strong> has sides with equal lengths. How can you be sure your hexagon is a regular hexagon?</p> <hr/> </section></section><section class="section2"><h2>Summary</h2> <p>A straightedge can be used to create line segments. Line segments are named by its endpoints.</p> <p>A compass can be used to create circles. Circles are named by its center and radius.</p> </section>