The Pythagorean Theorem

By Zachary Parkin

Pythagoras

• Pythagoras lived in the 500s BC.

• Was believed to prove the Pythagorean Theorem to be true.

The Formula

𝒂𝟐+𝒃𝟐=𝒄𝟐

CA

B

Babylonians understood the connection between the sides of a right triangle.

Babylonians figured out the relationship approximately 1000 years before Pythagoras.

It was named the Pythagorean Theorem because he is considered the first to have given proof that the formula is true.

History behind the Formula

Hypotenuse: The side opposite of the right angle.

Pythagorean Triples: It is when all sides are integer values. Example 3,4,5

Terms and Definitions

This formula can only be used with right triangles.

Two side lengths must be given.

When can it be used?

C5

12

It can be used to solve for any side. It is similarly used in Trigonometry

with In calculus, it is used in differentials.

Applications for the Formula

?

35

Parts of the Triangle

Hypotenuse

(C)Leg A

Leg B

Solve for C

1. 25+144=2. C=3. C=13

How to use the Formula

C

5

12

Solve for a

1. 49-36=2. a=

How to use the Formula continued…

7

a

6

Car A is traveling west

at 40 mi/h and car B is traveling north at 40 mi/h. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.4 mi and car B is 0.3 mi from the intersection?

Example of use for Differentials

Z

Y

X

1. ()2. 2x+2y=2z3. (x+y)/z= 4. =(40x+40y)/z

Solution

Given Values1. dx/dt=40 miles per

hour2. dy/dt=40 miles per

hourSolve for:Dz/dt when x=.4, and y=.3

Solve for z

1. =√.252. Z=.5 Plug the values into

=(40x+40y)/z1. =(16+12)/.52. =56 miles per hour

Solution Continued…

Z

.3

.4

http://www.mathblog.dk/pythagorean-triplets/ http://www.historyforkids.org/learn/greeks/scie

nce/math/pythagoras.htm http://

www.livius.org/a/1/greeks/pythagoras.JPG http://ualr.edu/lasmoller/pythag.html Problems given made up by Zachary Parkin

Works Cited

The End

Thank You