5.B: Pythagorean Theorem and Distance

Last updated
Save as PDF

Page ID: 31463

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$

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.

Watch

Pythagorean Theorem and Distance [8:55]

Do

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}">