1. 8-1 Pythagorean Theorem and the Converse

2. PYTHAGOREAN THEOREM c b a c a b What side is ALWAYS the c?
The HYPOTENUSE!!
(Remember it’s across from the 90.) a b
a and b are the legs. They can go in any order.

3. Pythagorean Triples!
A “triple” is a set of whole numbers that satisfy the Pythag. Thm.
Common Triples:
6-8-10

4. Example—Find c. c 6 8 It’s a Triple!! 6-8-10 62 + 82 = c2 36 + 64 = c2

5. Example– Find x 10 7
x = 100 x
It’s NOT a Triple!!

6. Example
What is the length of the hypotenuse of triangle ABC? Do the side lengths of triangle ABC form a Pythagorean Triple? Explain.

7. Word Problem– DRAW A PIC!!!!

8. Do the numbers form a Pythag. Triple?? (TWAP it out!) Hint: Plug into P. Thm to see if it works
1) 5, 7, 9 2) 10, 24, 26
Explain why!!!
Now, Let’s do The “Pythag. Converse”

9. RULES: c2 < a2 + b2. Acute (< 90) c2 > a2 + b2
RULES: c2 < a2 + b2 Acute (< 90) c2 > a2 + b2 Obtuse (> 90)
Remember that c is the longest side!
The “c” is in “c”harge!! It tells you the answer.
Is it a right, acute or obtuse triangle?
3, 6, 7
72___32+62
49>45 so its obtuse!
Try On Own: Is it right, acute, or obtuse?
20,21,28
5,6,8
20,21,29
Answers:
Acute 784<841
Obtuse 64>61
Right 841= 841

10. Be Careful with Rads! Which side is the longest? 4, √23, 8
√23 = 4.8 so 8 is the longest!!
What type of triangle is it?
64___ (Why is it 23?)
64>39 so it’s obtuse!

11. Homework
Pg # 7 – 31 odd