CCSS Grade 8 - Understand and apply the Pythagorean Theorem

  • 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.
  • 8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Example 1 - Benchmark Problem

I suggest having your students recreate this model so they can manipulate this in 3D.

PrismDiagonal-Benchmark.jpeg


Basics
It is important for students know the exact wording of the Pythagorean Theorem and what it means to write a legitimate proof. The Theorem page will explore the more familiar use of the theorem. Another idea that we need to explore is the Pythagorean Triple.
Applications
Application problems, like what you see below, are common to the school curriculum. The Diagonal of a LCD monitor problem uses a model from the 3D Ware house for a more realistic situation. The Diagonal of an Aquarium problem shows the dimensions for each of the points in the (x, y, z) format.

Example 2 - 2D - Diagonal of a LCD monitor

LCD Monitor Problem Page
What is the length of the monitor (reported as the length of the diagonal) to the nearest 1/4 of an inch?
Monitor.jpg


Example 3 - 3D - Diagonal of an Aquarium

What is the longest stick you could fit in an aquarium with these dimensions?
Find the length of the diagonal (shown in blue) inside the rectangular prism. Note that the dimensions reference the red, green and blue axis.
XrayPrism.jpg

Application with Trigonometry (and Slope)

The following section of text was found in the Standards section of the CORD geometry book. Think about how SketchUp could make the example for this Indiana State Standard much more realistic?

  • G.4.7 Find and use sides, perimeters, and areas of triangles, and relate these measures to each other using formulas.
Example: The gable end of a house is a triangle 20 feet long and 13 feet high. Find its area.

A more engaging problem would be to construct a house with these dimensions in the gable roof. Are the dimensions realistic? What is the pitch of this roof? Watch this video clip from the Internet to learn more about a gable roof and read this page to learn more about the pitch of a roof.
Checked June, 2014