<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <title>5.B: Pythagorean Theorem and Distance</title> <meta name="identifier" content="i0856bc4a622ebcb0d36c382d8314e762"/> <meta name="editing_roles" content="teachers"/> <meta name="workflow_state" content="active"/> </head> <body> <div id="HS21"> <div class="overview"> <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> </div> <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='<math xmlns="http://www.w3.org/1998/Math/MathML"> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>=</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> </math>' 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='<math xmlns="http://www.w3.org/1998/Math/MathML"> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> <mo>=</mo> <msup> <mi>d</mi> <mn>2</mn> </msup> </math>' 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='<math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </math>' 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='<math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <mspace width="mediummathspace" /> <msub> <mi>y</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </math>' 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='<math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>d</mi> <mo>=</mo> <msqrt> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>&#x2212;<!-- − --></mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>&#x2212;<!-- − --></mo> <msub> <mi>y</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> </math>' data-equation-content="d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}"> </li> </ul> </li> </ul> </div> </div> </body> </html>