Transcript Pythagorean Theorem and Calculating with Radicals

The Pythagorean Theorem
Chapter 6
The Pythagorean Theorem

In a right triangle, the square of the
length of the hypotenuse is equal to
the sum of the squares of the lengths
of the legs.
Converse of the
Pythagorean Theorem

If the lengths of the sides of a triangle
satisfy the relationship a2+b2=c2,
where c is the hypotenuse, then the
triangle is a right triangle.
Vocabulary



The number 9 is called a perfect square
since it is the square of the integer 3.
The number 3 is called a square root of 9
because 32=9.
The symbol
is called a radical sign. The
radical sign indicates the positive square
root of a number.


All positive numbers have two square roots.
Negative numbers do not have square roots.
12
48
75
3
4
7
24
2
2
8
4

A hot-air balloon is attached to a 75 foot rope
that is tied to a post. A breeze blows the balloon
to one side of the post, so that when the rope is
taut the balloon is over the edge of a flower bed
21 feet from the post. How high above the
flower bed is the balloon?
Homework