Pythagorean Theorem and Triples Notes
Recall: The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs equals
the square of the length of the hypotenuse.
A
C
B
Example 1) Find the missing side length. Express your answer in simplest radical form.
a)
b)
c)
Pythagorean Triples
A set of three nonzero whole numbers a , b , and c such that a 2  b 2  c 2 is called a Pythagorean Triple.
Examples of Common Triples
Example 2) Use Pythagorean triples to find the value of 𝑧.
Justify your answer.
a) 3, 4, 5
c) 8, 15, 17
13
4
12
b) 5, 12, 13
d) 7, 24, 25
(5z-2)
Pythagorean Word Problems
Example 3) A flagpole that was originally 24 feet tall has cracked 9 feet from the ground and has fallen as if hinged. Find
out how far from the base of the flagpole the top of the flagpole touched after it had fallen.
Example 4) A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top
of the ladder slips down 4 feet, how many feet will the bottom slide out?