Pythagorean TheoremPythagorean Theorem

By

Abdullah Alsowyan

Dr. Newberry

Have you ever thought in the length of each hypotenuse in the triangles on the rooftops?Do you know that if you know the length of two hypotenuse you can know the length of the third hypotenuse?

The history of PythagorasThe history of Pythagoras

He lived between 570 - 495 BC He was born on the island of Samos. He is a scientist in mathematician. There is a few information about his personal life. However, Pythagoras is now known as the finder of "Pythagoras Theorem" that it helps to find the value of the hypotenuse in right-angle triangles.

a2 + b2 = c2

About Pythagorean theoremAbout Pythagorean theoremAbout Pythagorean theoremAbout Pythagorean theorem

The definition of Pythagorean theorem is: in a right triangle, the square of the hypotenuse is equal to the squares of the two sides. In the math language:

A

BC

None of this shapes is rightNone of this shapes is right

What is the triangle that we are looking for?What is the triangle that we are looking for?

This shape and the similar of this shape are our targets This shape and the similar of this shape are our targets in Pythagorean theorem which should contain 90 in Pythagorean theorem which should contain 90 degrees by two sides of the triangle.degrees by two sides of the triangle.

9090

Example 1 Example 1

The equation said:

a2 + b2 = c2

(4x4) + (5x5) = c2

16 + 20 = 36

√36 = 6

C = 6A = 4

B = 5C = ?

Example 2Example 2

A = 6

C = 10B = ?

The equation said:

a2 + b2 = c2

(6*6) + b2 = (10*10)

36 + b2 = 100

36 + 64 = 100

√64 = 8

b = 8

Try by yourself:Try by yourself:

A = 8

B = 10

C = ?

Solve the problem and after you done click on the mouse:

Sorry, this is not right triangle

Try by yourself 2:Try by yourself 2:

A = 3

B = 4

Solve the problem and after you done click on the mouse:

The equation said:

a2 + b2 = c2

(3x3) + (4x4) = c2

9 + 16 = 36

√25 = 5

C = 5

C = ?

Review:Review:

- We can use Pythagorean theorem with the right triangle.- The equation of the Pythagorean theorem is a2 + b2 = c2

- The right triangle is a triangle that containing an angle of 90 degrees.- By using Pythagorean theorem we can know the value of A, B or C if we known the value of two of them

Helpful Link:Helpful Link:

http://www.regentsprep.org/regents/math/geometry/gp13/Pythag.htm

http://www.cut-the-knot.org/pythagoras/index.shtml

Pythagorean Theorem - MathHelp.com - Geometry Help

The Objectification of the Right-angled Triangle in the Teaching of the Pythagorean Theorem: An Empirical Investigation

Thank you