1. The Pythagorean Theorem

2. Right Triangles
The two sides that form the right angle are called legs.
The side opposite the right angle is called the hypotenuse.
The legs are the two shorter sides.
Hypotenuse
Leg
The hypotenuse is the longest side.
Leg

3. The Pythagorean Theorem
A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.
Hypotenuse
Leg
Leg

4. Instructions
1. On the left side of your paper, draw and color in a 4x4 square. 4 16 4
Write in the dimensions of this square.
3. Find the AREA of the square and write it in the square.

5. Instructions
4. Draw a 3 unit line extending from the bottom of the square. 4 16 4 3 9
5. Label the dimensions of this line.
6. Make a square and write in the AREA of this square.

6. Instructions
7. Let 3 and 4 be the legs of a triangle, now draw a hypotenuse. 4 5 16 4 3 9
8. How many units long is the hypotenuse? Cut your paper and line it up to see.

7. Instructions
9. Color a 5x5 square on your extra paper, and cut it out. 4 25 5 25 16 5 4 3 9
10. Find the area of this square and label it.
11. Move your square over to the hypotenuse.

8. Observations?
Do you NOTICE anything about the area’s of the three squares? 4 25
ADD up 16 5 4
= 25! 3 9
So, the area of a square made by the LEGS equals the area of a square made by the hypotenuse.
THUS, a2 + b2 = c2

9. The Pythagorean Theorem
ONLY works for RIGHT TRIANGLES!!
NO!
YES!
YES!
NO!
YES!