About This Chapter
Standard: Explain a proof of the Pythagorean Theorem and its converse. (CCSS.MATH.CONTENT.8.G.B.6)
Standard: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (CCSS.MATH.CONTENT.8.G.B.7)
Standard: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (CCSS.MATH.CONTENT.8.G.B.8)
About This Chapter
Students who have reached these Common Core standards will understand the Pythagorean Theorem and its use in finding unknown lengths and distances. The lessons in this chapter help students learn about the following:
- Definition and uses of the Pythagorean Theorem
- Converse of the theorem
- Special cases concerning the theorem
- Applying the theorem
- Using the theorem to find distance
You'll know that your eighth graders have mastered this standard when they are able to explain a proof of both the Pythagorean Theorem and its converse, as well as use the theorem to find side lengths in right triangles and the distance between two separate points in a coordinate system.
How to Use These Lessons in Your Classroom
The following suggestions will help you implement these resources into your classroom curriculum in order to meet the Common Core standards.
Hold a Pythagorean Scavenger Hunt
Watch the lessons about the Pythagorean Theorem and its applications. Let students search the classroom for objects that appear to have right angles. Have students measure two of the sides, then use the theorem to find the length of the third side. Measure the side in question and compare it to the value found using the theorem to judge whether or not they have truly located a right triangle.
Create Distance Problems
Have students view the lesson 'Finding Distance with the Pythagorean Theorem.' Building off the examples in the lesson, have students work in small groups to design their own distance problems that can be solved using the Pythagorean Theorem. After they've finished, have groups trade work with one another and attempt to answer each other's questions.
Supplement Instruction With Lesson Videos
Students who are struggling to understand a concept often benefit from having the topic explained in a different way. Show the video lessons in addition to your regular classroom instruction to provide alternative approaches to lesson topics.
1. Pythagorean Theorem: Definition & Example
Learn what the Pythagorean Theorem says about a right triangle and the relationships of its three sides to each other by watching this video lesson. Also learn how you can use this to your advantage when solving problems.
2. The Pythagorean Theorem: Converse and Special Cases
The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.
3. The Pythagorean Theorem: Practice and Application
The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.
4. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
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Other chapters within the Common Core Math Grade 8 - Geometry: Standards course