## Day 8 The Pythagorean Theorem

### Objectives:

1) Use of the Pythagorean Theorem

2) Use of the converse of the Pythagorean Theorem

### 1) Draw a right triangle represented with geometric squares
as follows:

### The sides of the right triangle have lengths 3, 4, and 5 units.
The area of the larger square is equal to the total area of the
two smaller squares.

### This relationship is true for any right triangle

### Have the students explore this concept with various size triangles
to show this is true.

### 2) State the Pythagorean Theorem

### Pythagorean Theorem: In a right triangle, the square of the
length of the hypotenuse *c *is equal to the sum of the squares
of the lengths of the legs *a* and *b*.

### Symbols:

###

### Practice Problem: Find the length of
the hypotenuse of several right triangles.

###

### 3) Explain to the students the converse of the Pythagorean
Theorem

### Converse of the Pythagorean Theorem: If *c* is the measure
of the longest side of a triangle, *a* and *b* are the
lengths of the other two sides, and ,
then the triangle is a right triangle.

### Have the students determine whether certain triangles are
right triangles using the converse of the Pythagorean Theorem.

### Practice Problem: The lengths of the
three sides of a triangle are 5, 7, and 9 inches. Determine whether
this triangle is a right triangle.