1. Warm-Up
Find the group members with the same letter on their worksheet as you.
Complete problems #3 & #4.
Take your homework with you to be checked!

2. Homework Answers - Friday

4. Section 8.2 Notes: The Pythagorean Theorem and its Converse

5. Pythagorean Theorem

6. Example 1: Find the value of x.

7. Example 1: Find the value of x.b)

8. Pythagorean Triples
 6,8,10
10,24,26 
 16,30,34
 14,48,50
 9,12,15
 15,36,39
 24,45,51
 21,72,75
 12,16,20
 20,48,52
 32,60,68
28,96,100

9. Example 2:
Use a Pythagorean Triple to find the value of x. a)

10. Example 2:
Use a Pythagorean Triple to find the value of x. b)

11. Example 3:
a) A 20-foot ladder is placed against a building to reach a window that is 16 feet above the ground. How many feet away from the building is the bottom of the ladder?

12. Example 3:
b) A 10-foot ladder is placed against a building. The base of the ladder is 6 feet from the building. How high does the ladder reach on the building?

13. In ∆𝐴𝐵𝐶 with side lengths a, b, c: (c is longest side)
Converse of the Pythagorean Theorem
 If 𝑎 2 + 𝑏 2 = 𝑐 2 , then ∆𝐴𝐵𝐶 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒.
Pythagorean Inequality Theorem 8.6
 If 𝑎 2 + 𝑏 2 > 𝑐 2 , then ∆𝐴𝐵𝐶 𝑖𝑠 𝑎𝑛 𝑎𝑐𝑢𝑡𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒.  
Pythagorean Inequality Theorem 8.7
 If 𝑎 2 + 𝑏 2 < 𝑐 2 , then ∆𝐴𝐵𝐶 𝑖𝑠 𝑎𝑛 𝑜𝑏𝑡𝑢𝑠𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒.
You must verify that if forms ANY triangle first!

14. Example 4:
a) Determine whether 9, 12, and 15 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

15. Example 4:
b) Determine whether 10, 11, and 13 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

16. Pythagorean Theorem Post-It Activity

17. Summary!
If , then ABC is
_____________.

18. Summary!
1. Are the triangles obtuse, right, or acute? a)

19. Summary!
1. Are the triangles obtuse, right, or acute? b)