1. Unit 7A - Lesson #4: Pythagorean Theorem (Textbook Section 7-2)
Please pick up and complete the Lesson #4: Right Triangle Investigation example sheet found on the front table.
Grab a Ruler and Calculator as well.

2. Leg Investigation Hypotenuse 3 4 5 25 25 6 8 10 100 5 12 1 3 169 Leg1
Leg1
Leg2
Hypotenuse
(Leg1)2 + (Leg2)2
Hypotenuse2
Triangle #1  3  4 5 
25 
 25
Triangle #2  6  8
10 
100 
Triangle #3  5
12 
1 3
169 
Leg
Hypotenuse

3. c a b Pythagorean Theorem
In any right triangle with leg lengths of a and b, and a hypotenuse with length c, then a2 + b2 = c2. a b c

4. Pythagorean Triples
Sets of three whole numbers that are known to form a right triangle.
Famous Triples
3, 4 ,5
5, 12, 13
8, 15, 17
7, 24, 25
Doubled
6, 8, 10
10, 24, 26
16, 30, 34
14, 48, 50
Tripled
9, 12, 15
15, 36, 39
24, 45, 51
21, 72, 75

5. Example #1: Determining Right TrianglesNo
Yes
(A) 3, 7, 8 _______ (B) 10, 24, 26 _______
 82
 64
58  64
= 262
= 676
676 = 676
Power of Pythagorean Triples:
(5, 12, 13)  2 = 10, 24, 26

6. Example #1: Determining Right Triangles
Yes No
(C) _______ (D) 6, 11, 9 _______
 112
 121
117  121

7. Using the Pythagorean Theorem
Finding the Hypotenuse 4 3 x
Pythagorean Triple:
3, 4, 5

8. Power of Pythagorean Triples
x = 1521
x2 = 225 y 36 39
3 = 13
3 = 12
Pythagorean Triple?
?, 12, 13 or 12, ?, 13
5, 12, 13 3 15

9. Exact Answers

10. Examples of the Pythagorean Theorem
Finding a Leg
x = 172
x = 289
x2 = 208 x 9 17
(Exact Answer)
(Approximate)

11. Example #2: Using the Pythagorean Thm.15
(A) x = _________ (B) x = _________
x  ________ x  ________
10.6
Not Needed
= x2
122 + y2 = 162
Pyth. Triple?
9  3 = 3
12  3 = 4
Look for: 3, 4, ?
3, 4, 5 3 15

12. Example #2: Using the Pythagorean Thm.30 4
(C) z = _________ (D) w = _________
z  ________ w  ________
Not Needed
Not Needed
z = 342
= w2 34 z 16
z2 = 900
= w2
16 = w2 2 w
Pyth. Triple?
16  2 = 8
34  2 = 17
Look for:
?, 8, 17 or 8, ?, 17
8, 15, 17 2 30

13. Example #3: Right Triangles in Polygons
(A) x = _________ 14 12 x
w = 142 6 6

14. Example #3: Right Triangles in Polygons
(B) Perimeter = _________________ 10 16 9 3 x
= x2

15. Example #4
A farmer is 5’ 7” tall. He wants to clean a spot 13 feet up on inside of his silo that has developed some mold. He currently has a 10 foot ladder. Will he be able to reach the spot with his current equipment? Write a response using complete sentences, proper spelling, grammar, and punctuation.
Things to Consider:
Spacing of the rungs on the ladder?
How many rungs up can the farmer use?
How close is the base of the ladder to the silo wall?

16. Example #4
Forming a right triangle with the ladder and the silo wall, we can use the Pythagorean Theorem to determine how high up the wall the ladder reaches. Adding the farmer’s height of 5’7”, it is reasonable to say that he will be able to reach the mold.
Ground
Silo Wall
Ladder
Triangle #1
 0.5
9.98 10
Triangle #2  1
9.95
Triangle #3
 1.5
9.89
Triangle #4  2
9.8
Triangle #5
 2.5
9.68
Triangle #6  3
9.54
Triangle #7
 3.5
9.37
Triangle #8  4
9.16
Triangle #9
 4.5
8.93
Triangle #10  5
8.66
Triangle #11
 5.5
8.35
SiloWall
Ground
Ladder
(10 feet)