5.B: Pythagorean Theorem and Distance
- Page ID
- 31463
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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.
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
- In three dimensions, the Pythagorean Theorem is
- The distance between two points can be found using the Pythagorean Theorem.
- The distance between and is </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}">