Chapter 6: Pythagorean Theorem
Overview:
This unit explores the Pythagorean Theorem in mathematical and real-world contexts in both 2- and 3-Dimensions. Proofs of the Pythagorean Theorem are also investigated and students learn to apply the Pythagorean Theorem to find distance in the coordinate plane.
This unit explores the Pythagorean Theorem in mathematical and real-world contexts in both 2- and 3-Dimensions. Proofs of the Pythagorean Theorem are also investigated and students learn to apply the Pythagorean Theorem to find distance in the coordinate plane.
Common Core Learning Standards:
- 8.G.6. Explain a proof of the Pythagorean Theorem and its converse.
- 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.
LESSONS 6.1-6.6: LEARNING GOALS
Lesson 1- Pythagorean Theorem (2 days) Learning Objectives (skills):
Learning Objectives (skills):
Learning Objectives (skills):
Learning Objectives (skills):
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What was up with Pythagoras? by Vi HartWhile the whole video is interesting, you may skip ahead to the 3:09 mark and begin watching from there. In this YouTube clip, Vi Hart explains the Pythagorean Theorem using doodles and manipulatives.
This video will provide you with a jump start into this unit by explaining what you will be learning about and why it makes sense, while also requiring you to remember properties of the real number system (like irrational numbers) and how they relate to the Pythagorean Theorem. |
Lessons & Links
Lesson 6.1: The Pythagorean Theorem (pg. 313-334)
Videos:
What is a Theorem?
What is the Pythagorean Theorem?
What are the Legs and Hypotenuse of a Right Triangle?
Lesson 6.2: The Converse of the Pythagorean Theorem (pg. 335 - 342)
Videos:
How do you determine if a triangle is a right triangle when you know the length of the sides?
6.1/6.2 Extra Practice:
Download File
Lesson 6.4: Distance Between Two Points in a Coordinate System (pg. 349 - 356)
Videos:
6.5: Diagonals in 2D/Multistep Application Problems w/Area (pg. 357-364)
Videos:
Lesson 6.6: Diagonals in Three Dimensions (pg. 365-376)
Videos:
Apply the Pythagorean Theorem to three dimensional figures using right triangles
3D Pythagorean Theorem (Prisms)
Videos:
What is a Theorem?
What is the Pythagorean Theorem?
What are the Legs and Hypotenuse of a Right Triangle?
Lesson 6.2: The Converse of the Pythagorean Theorem (pg. 335 - 342)
Videos:
How do you determine if a triangle is a right triangle when you know the length of the sides?
6.1/6.2 Extra Practice:
Download File
Lesson 6.4: Distance Between Two Points in a Coordinate System (pg. 349 - 356)
Videos:
6.5: Diagonals in 2D/Multistep Application Problems w/Area (pg. 357-364)
Videos:
Lesson 6.6: Diagonals in Three Dimensions (pg. 365-376)
Videos:
Apply the Pythagorean Theorem to three dimensional figures using right triangles
3D Pythagorean Theorem (Prisms)
Documents & Files
Pythagorean Theorem Prezi
Visual Proofs of the Pythagorean Theorem
Visual Proofs of the Pythagorean Theorem
- Visual Proof 1: Water Demo (embedded below, too)
- Visual Proof 2: Starbursts (embedded below, too)
- Visual Proof 3: Origami (embedded below, too)
Ch 6 Extra Practice
6.1-6.2_extra_practice.pdf |
Chapter 6 Practice Test & Answer Key
m8_ch6_test_review.pdf |
8th_grade_chapter_6_review_answer_key.pdf |