lesson 8.1: pythagorean theorem. pythagorean theorem pythagorean theorem:
TRANSCRIPT
![Page 1: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/1.jpg)
Lesson 8.1: Pythagorean Theorem
![Page 2: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/2.jpg)
Pythagorean Theorem
• Pythagorean Theorem:
![Page 3: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/3.jpg)
Practice
• What is the length of each missing side?
![Page 4: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/4.jpg)
SOL Question
• What is the length of theunlabeled side?
![Page 5: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/5.jpg)
Reducing Radicals
• Reducing Radicals:
• Ex: Reduce each radical:√45 √12 √72
![Page 6: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/6.jpg)
Practice
Reduce each radical:√12 = √18 =
√25 = √50 =
√27 = √20 =
![Page 7: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/7.jpg)
√28 = √63 =
√75 = √1 =
√8 = √6 =
Practice
![Page 8: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/8.jpg)
Practice
• Find the missing side length of each triangle. Put solutions in simplest radical form.
4m 6m 10m
5m
![Page 9: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/9.jpg)
Application
ABCD represents a lawn with a sidewalk. How much shorter is walking across the lawn from A to D than walking along the sidewalk?
A B
C D100m
300m
![Page 10: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/10.jpg)
Converse of the Pythagorean Theorem
Converse of the Pythagorean Theorem:
Right:
Acute:
Obtuse:
![Page 11: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/11.jpg)
Practice
![Page 12: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/12.jpg)
Extension – Possible Side Length
• Ex: A triangle has side lengths 6 and 8. What must the third side be for a right triangle?
• A triangle has side lengths 5 and 12. What must the third side be for an obtuse triangle?
![Page 13: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/13.jpg)
Classwork
• Lesson 8.1, #1 – 14
![Page 14: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/14.jpg)
Special Right Triangles (part 1)
• 45 – 45 – 90 Triangle:
![Page 15: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/15.jpg)
Practice
• What is the length of each missing side?
5m12m
![Page 16: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/16.jpg)
Challenge
• Find the length of AC.
45o
45o
18m
36m
A B C
D
![Page 17: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/17.jpg)
Bonus: Pythagorean Triples
• Pythagorean Triples:
![Page 18: Lesson 8.1: Pythagorean Theorem. Pythagorean Theorem Pythagorean Theorem:](https://reader030.vdocuments.us/reader030/viewer/2022013103/56649d345503460f94a0b141/html5/thumbnails/18.jpg)
Homework
• Lesson 8.1 #17 – 35 oddLesson 8.2, #7 – 11 odd
• Lesson 8.2, #15 – 33 odd