LT 6.1 Pythagorean Triples
Pythagorean Triple
A Pythagorean triple is a set of positive integers a, b, and c that satisfy the equation
. This means
that a, b, and c are the legs and hypotenuse of a right triangle. Right triangles that have non-integer sides will
not form Pythagorean Triples.
We name Pythagorean triples by “families.” For example, the most common family is the
triangle.
Verify that those are the sides of a right triangle.
Some other members of the
Why are these considered part of the
family are shown below.
family?
How can you use a family to find new right triangles? To find a missing side of a right triangle?
Other common families of Pythagorean Theorem are listed below:
right
Use Pythagorean triples to find the missing sides.
1. Family:
2. Family:
3. Family:
Find the missing side of each right triangle in simplified radical form. Determine if the sides form a
Pythagorean triple. If so, name the family it comes from.
4.
5.
c = ______
Triple? ______
Family: _________
6.
c = ______
Triple? ______
Family: _________
7.
c = ______
Triple? ______
Family: _________
8.
c = ______
Triple? ______
Family: _________
9.
c = ______
Triple? ______
Family: _________
c = ______
Triple? ______
Family: _________