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<title>5.B: Pythagorean Theorem and Distance</title>
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<h2>Overview</h2>
<p>The purpose of this lesson is to apply the Pythagorean Theorem to various situations in two and three dimensions.</p>
<p>This lesson will address the following CCRS Standard(s) for Geometry:</p>
<ul>
<li><em>8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions</em></li>
</ul>
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<div class="directions">
<h2>Directions</h2>
<ol>
<li>Take notes while watching videos below</li>
<li>Go to <a class="external" href="http://wamap.org/" target="_blank">http://wamap.org</a> and log into our course to complete assignment 5.C with 80% or better.</li>
</ol>
</div>
<h3>Watch</h3>
<p><a class="" href="https://youtu.be/uFTNeI-lpNU">Pythagorean Theorem and Distance [8:55]</a></p>
<h3>Do</h3>
<p>Complete assignment 5.C with 80% or better at <a href="http://wamap.org">http://wamap.org</a></p>
<div class="summary">
<h2>Summary</h2>
<p>In this lesson we have learned:</p>
<ul>
<li>In two dimensions, the Pythagorean Theorem is <img class="equation_image" title="a^2+b^2=c^2" src="https://sbctc.instructure.com/equation_images/a%255E2%2Bb%255E2%253Dc%255E2" alt="LaTeX: a^2+b^2=c^2" data-mathml='&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;
  &lt;msup&gt;
    &lt;mi&gt;a&lt;/mi&gt;
    &lt;mn&gt;2&lt;/mn&gt;
  &lt;/msup&gt;
  &lt;mo&gt;+&lt;/mo&gt;
  &lt;msup&gt;
    &lt;mi&gt;b&lt;/mi&gt;
    &lt;mn&gt;2&lt;/mn&gt;
  &lt;/msup&gt;
  &lt;mo&gt;=&lt;/mo&gt;
  &lt;msup&gt;
    &lt;mi&gt;c&lt;/mi&gt;
    &lt;mn&gt;2&lt;/mn&gt;
  &lt;/msup&gt;
&lt;/math&gt;' data-equation-content="a^2+b^2=c^2">
</li>
<li>In three dimensions, the Pythagorean Theorem is <img class="equation_image" title="a^2+b^2+c^2=d^2" src="https://sbctc.instructure.com/equation_images/a%255E2%2Bb%255E2%2Bc%255E2%253Dd%255E2" alt="LaTeX: a^2+b^2+c^2=d^2" data-mathml='&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;
  &lt;msup&gt;
    &lt;mi&gt;a&lt;/mi&gt;
    &lt;mn&gt;2&lt;/mn&gt;
  &lt;/msup&gt;
  &lt;mo&gt;+&lt;/mo&gt;
  &lt;msup&gt;
    &lt;mi&gt;b&lt;/mi&gt;
    &lt;mn&gt;2&lt;/mn&gt;
  &lt;/msup&gt;
  &lt;mo&gt;+&lt;/mo&gt;
  &lt;msup&gt;
    &lt;mi&gt;c&lt;/mi&gt;
    &lt;mn&gt;2&lt;/mn&gt;
  &lt;/msup&gt;
  &lt;mo&gt;=&lt;/mo&gt;
  &lt;msup&gt;
    &lt;mi&gt;d&lt;/mi&gt;
    &lt;mn&gt;2&lt;/mn&gt;
  &lt;/msup&gt;
&lt;/math&gt;' data-equation-content="a^2+b^2+c^2=d^2">
</li>
<li>The distance between two points can be found using the Pythagorean Theorem. 
<ul>
<li>The distance between <img class="equation_image" title="\left(x_1,y_1\right)" src="https://sbctc.instructure.com/equation_images/%255Cleft%2528x_1%252Cy_1%255Cright%2529" alt="LaTeX: \left(x_1,y_1\right)" data-mathml='&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;
  &lt;mrow&gt;
    &lt;mo&gt;(&lt;/mo&gt;
    &lt;mrow&gt;
      &lt;msub&gt;
        &lt;mi&gt;x&lt;/mi&gt;
        &lt;mn&gt;1&lt;/mn&gt;
      &lt;/msub&gt;
      &lt;mo&gt;,&lt;/mo&gt;
      &lt;msub&gt;
        &lt;mi&gt;y&lt;/mi&gt;
        &lt;mn&gt;1&lt;/mn&gt;
      &lt;/msub&gt;
    &lt;/mrow&gt;
    &lt;mo&gt;)&lt;/mo&gt;
  &lt;/mrow&gt;
&lt;/math&gt;' data-equation-content="\left(x_1,y_1\right)"> and <img class="equation_image" title="\left(x_2,\:y_2\right)" src="https://sbctc.instructure.com/equation_images/%255Cleft%2528x_2%252C%255C%253Ay_2%255Cright%2529" alt="LaTeX: \left(x_2,\:y_2\right)" data-mathml='&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;
  &lt;mrow&gt;
    &lt;mo&gt;(&lt;/mo&gt;
    &lt;mrow&gt;
      &lt;msub&gt;
        &lt;mi&gt;x&lt;/mi&gt;
        &lt;mn&gt;2&lt;/mn&gt;
      &lt;/msub&gt;
      &lt;mo&gt;,&lt;/mo&gt;
      &lt;mspace width="mediummathspace" /&gt;
      &lt;msub&gt;
        &lt;mi&gt;y&lt;/mi&gt;
        &lt;mn&gt;2&lt;/mn&gt;
      &lt;/msub&gt;
    &lt;/mrow&gt;
    &lt;mo&gt;)&lt;/mo&gt;
  &lt;/mrow&gt;
&lt;/math&gt;' data-equation-content="\left(x_2,\:y_2\right)"> is <img class="equation_image" title="d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}" src="https://sbctc.instructure.com/equation_images/d%253D%255Csqrt%257B%255Cleft%2528x_1-x_2%255Cright%2529%255E2%2B%255Cleft%2528y_1-y_2%255Cright%2529%255E2%257D" alt="LaTeX: d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}" data-mathml='&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;
  &lt;mi&gt;d&lt;/mi&gt;
  &lt;mo&gt;=&lt;/mo&gt;
  &lt;msqrt&gt;
    &lt;msup&gt;
      &lt;mrow&gt;
        &lt;mo&gt;(&lt;/mo&gt;
        &lt;mrow&gt;
          &lt;msub&gt;
            &lt;mi&gt;x&lt;/mi&gt;
            &lt;mn&gt;1&lt;/mn&gt;
          &lt;/msub&gt;
          &lt;mo&gt;&amp;#x2212;<!-- − -->&lt;/mo&gt;
          &lt;msub&gt;
            &lt;mi&gt;x&lt;/mi&gt;
            &lt;mn&gt;2&lt;/mn&gt;
          &lt;/msub&gt;
        &lt;/mrow&gt;
        &lt;mo&gt;)&lt;/mo&gt;
      &lt;/mrow&gt;
      &lt;mn&gt;2&lt;/mn&gt;
    &lt;/msup&gt;
    &lt;mo&gt;+&lt;/mo&gt;
    &lt;msup&gt;
      &lt;mrow&gt;
        &lt;mo&gt;(&lt;/mo&gt;
        &lt;mrow&gt;
          &lt;msub&gt;
            &lt;mi&gt;y&lt;/mi&gt;
            &lt;mn&gt;1&lt;/mn&gt;
          &lt;/msub&gt;
          &lt;mo&gt;&amp;#x2212;<!-- − -->&lt;/mo&gt;
          &lt;msub&gt;
            &lt;mi&gt;y&lt;/mi&gt;
            &lt;mn&gt;2&lt;/mn&gt;
          &lt;/msub&gt;
        &lt;/mrow&gt;
        &lt;mo&gt;)&lt;/mo&gt;
      &lt;/mrow&gt;
      &lt;mn&gt;2&lt;/mn&gt;
    &lt;/msup&gt;
  &lt;/msqrt&gt;
&lt;/math&gt;' data-equation-content="d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}">
</li>
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</li>
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