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The Pythagorean Theorem

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Anisa Rodriguez

on 9 January 2014

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Transcript of The Pythagorean Theorem

The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations.Not only is it one of the most famous contributions to the mathematical community, but it is among one of the most important. It is a concept that is still used to this day. It assists in solving real life problems and the ones you see on your homework. In this visual presentation, the exploration of the Pythagorean Theorem is one that begins with three basic questions:

Who was Pythagoras?
What is a triangle?
What is the Pythagorean Theorem and how do we use it?
The Pythagorean Theorem
Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece.
He was an Ionian Greek philosopher and mathematician.

Additionally, Pythagoras founded the religious movement called Pythagoreanism. Its followers were devout to the study of mathematics. They pursued the religious rites and practices developed by Pythagoras, and studied his philosophical theories. One of his theorems that are still used and studied to this day as it was during his time is the Pythagorean Theorem.
C- the hypotenuse (longest side) of the triangle (you can always identify the hypotenuse by locating the right angle; the hypotenuse the side opposite from the right angle).

A & B- the "legs" of the triangle

(A is usually the shortest side of the triangle, while B is the remaining side of the figure- the non-hypotenuse)

The Pythagorean Theorem is used to solve for any unknown side of a right triangle.

When presented with a problem, using the Pythagorean theorem can be simple. For instance, if you are given the value of two out of the three sides of a right triangle, you would apply the Pythagorean theorem by substituting the corresponding variables and solve for the one that is missing. You must be sure to find the square root of your answer in order for it to be correct. All the while referring to the model:

a2 + b2= c2
(A squared plus B squared equals C squared)
Example 2
three vertices
An interior angle sum of 180 degrees
Classification by sides and by interior angles (i.e. right triangle, acute,isosceles, obtuse, etc.)
*It is necessary to know what a triangle is before learning the Pythagorean Theorem
The Pythagorean theorem deals with right triangles, which is a type of triangle that was mentioned in the previous slide. A right triangle has one right angle (equivalent to 90 degrees). The Pythagorean Theorem tells us that if we're dealing with right triangles, then the relationship between their sides is:

a2 + b2 = c2
(A squared plus B squared equals C squared)

What is the Pythagorean Theorem?
Example 1
Example 3
Explaining the Pythagorean Theorem
How to Use the Pythagorean Theorem
Who is Pythagoras?
Who is Pythagoras? (continued)
"A plane figure with three straight sides and three angles"
The definition of a Triangle is:
Every triangle also has:
*However this is if, and ONLY if the figure is a right triangle!
Solving for C
(the hypotenuse)
Solving for A or B (the shorter sides of the triangle)
Using the Pythagorean Theorem to solve real life problems
By Anisa Rodriguez
Thank you for watching, I hope this presentation was informative and enjoyable!:)
Full transcript