Lesson 12.5 Notes: The Pythagorean Theorem and Its Converse
Review: Simplify each expression.
1) √
2) √
3)
√
√
Right Triangle:

A triangle with a ______ (right) angle.

The ___________ are the sides of the triangle that are adjacent to the right angle.

The ______________________ is side of the triangle that is opposite of the right angle. It is
also the ________________ side of the right triangle.
Pythagorean Theorem:

If a triangle is a right triangle, then the sum of the squares of the lengths of the legs
and
equals the square of the length of the hypotenuse .

In other words,
Examples: Find the missing length of the right triangle if
the length of the hypotenuse.
4)
5)
6)
7)
and
are the lengths of the legs and
is
Examples: Use the Pythagorean Theorem to find each missing length.
8)
9)
Converse of the Pythagorean Theorem:

If a triangle has side lengths
and
such that
, then the triangle is a
____________ triangle.
Examples: Determine whether the given lengths are sides of a right triangle.
10)
11)
Multiple Choice Practice:
12) The line plot below shows the number of hours each person in Mr. Finley's class studied for an exam. What is the
median of the data in the graph?
(Each X represents one student.)
A. 4 hours
B. 3 hours
C. 5 hours
D. 3.5 hours