Name:
5D
Date:
Read:
A Pythagorean triple is three whole numbers that satisfy the equation a
2
+ b
2
= c
2
where c is the greatest number.
If the measures of the sides of any right triangle are whole numbers, the measures form a Pythagorean triple.
Examples:
Which of these sets of measures form the sides of a right triangle? Which of these sets form a Pythagorean triple?
1.
3, 4, and 5 2.
8, 15, and 16 3.
5
6
, ,
5 5 a
2
+ b
2
3
2
+ 4
2
= c
2
= 5
2 a
2
8
2
+ b
2
+ 15
2
= c
2
= 16
2

-------
5
3 
2
+

-------
5

2
=
 
5
2
9 + 16 = 25
25 = 25
64 + 225 = 256
289

256
25
+
25
=
25
• In example 1, the segments form the sides of a right triangle since they satisfy the Pythagorean theorem. The measures are whole numbers and form a Pythagorean triple.
• In example 2, the segments with these measures cannot form a right triangle. Therefore, they do not form a
Pythagorean triple.
• In example 3, the segments with these measures form a right triangle. However, the three numbers are not whole numbers. Therefore, they do not form a Pythagorean triple.
Practice:
Determine if the following segments form a right triangle and determine if they are Pythagorean triples:
1.
5, 12, and 13
2.
8, 15, and 17
3.
1, 2, and 3
4.
12, 35, and 37
5.
4, 16, and 4 17
5D Pythagorean Triples

6.
7, 24, and 25
7.
When we take multiples of the Pythagorean triples above, they form new Pythagorean triples. These new
Pythagorean triples are considered families of the original triple. For example, you found that 3, 4, and 5 formed a triple. If you multiple each of these by a whole number (other than zero) you will find new triples.
An example is 18, 24,and 30.
a.
How was this triple formed? b.
Use the triples in #1, to find at two additional triples in the same family.
c.
Use the triples in #2, to find two additional triples in the same family.
5D Pythagorean Triples