1. Lesson 8.1: Pythagorean Theorem

2. Pythagorean Theorem
Pythagorean Theorem:

3. Practice
What is the length of each missing side?

4. SOL Question
What is the length of the unlabeled side?

5. Reducing Radicals Reducing Radicals:
Ex: Reduce each radical: √45 √ √72

6. Practice
Reduce each radical:
√12 = √18 =
√25 = √50 =
√27 = √20 =

7. Practice
√28 = √63 = √75 = √1 = √8 = √6 =

8. Practice
Find the missing side length of each triangle. Put solutions in simplest radical form.
4m m
10m 5m

9. Application
A B
C D
ABCD represents a lawn with a sidewalk. How much shorter is walking across the lawn from A to D than walking along the sidewalk?
300m
100m

10. Converse of the Pythagorean Theorem
Converse of the Pythagorean Theorem: Right: Acute: Obtuse:

11. 
Practice

12. 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?

13. Classwork
Lesson 8.1, #1 – 14

14. Special Right Triangles (part 1)

15. Practice
What is the length of each missing side?
12m 5m

16. Challenge
Find the length of AC. D
45o
36m
45o
A B C
18m

17. Bonus: Pythagorean Triples

18. Homework Lesson 8.1 #17 – 35 odd Lesson 8.2, #7 – 11 odd