Download Families of Right Triangles 1. Pythagorean Triples

Geometry Notes 9.6: Families of Right Triangles
1. Pythagorean Triples: Any three whole numbers that satisfy the equation
a 2 + b 2 = c 2 form a Pythagorean Triple.
Basic Families
(3, 4, 5)
(5, 12, 13)
Multiples of the Basic Families:
(6,8,10)
(10,24,26)
(9,12,15)
(15,36,39)
(12,16,20)
(20,48,52)
(15,20,25)
(25,60, 65)
(18, 24, 30)
(30,72,78)
(8, 15, 17)
( 7, 24, 25)
(16,30,34)
(24,45,51)
(32,60,68)
(40,75, 85)
(48, 90,102)
(14,48,50)
(21,72,75)
(28,96,100)
(35,120,125)
(42,144, 150)
Other families:
(9, 40, 41)
(20, 21, 29)
(12, 35, 37)
(11, 60, 61)
2. Principle of the reduced triangle: Not all problems are solved by triples, and
using the Pythagorean theorem can be tedious. If all the numbers can be
multiplied or divided by a common number, you can create a triangle that is easier
to work with.
a. Multiply or divide all of the sides by the same number.
b. Solve the new simplified triangle.
c. To revert back to the original triangle, use the opposite operation.
77
b
Sample:
55
x
4
7
1
2