5.B: Pythagorean Theorem and Distance

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Overview

The purpose of this lesson is to apply the Pythagorean Theorem to various situations in two and three dimensions.

This lesson will address the following CCRS Standard(s) for Geometry:

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

Directions

Take notes while watching videos below
Go to http://wamap.org and log into our course to complete assignment 5.C with 80% or better.

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Pythagorean Theorem and Distance [8:55]

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Complete assignment 5.C with 80% or better at http://wamap.org

Summary

In this lesson we have learned:

In two dimensions, the Pythagorean Theorem is $a^{2} + b^{2} = c^{2}$
In three dimensions, the Pythagorean Theorem is $a^{2} + b^{2} + c^{2} = d^{2}$
The distance between two points can be found using the Pythagorean Theorem.
- The distance between $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $d = \sqrt{(x_{1} -}$ </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>−</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}">