Pythagorean Theorem Rachel Griffith. Pythagoras was a Greek philosopher and mathematician who founded the Pythagorean Theorem. He also discovered the.

Pythagorean Pythagorean TheoremTheorem

Rachel GriffithRachel Griffith

Pythagoras was a Greek philosopher and mathematician who founded the Pythagorean Pythagoras was a Greek philosopher and mathematician who founded the Pythagorean Theorem. He also discovered the relationship between math and the sounds of strings on Theorem. He also discovered the relationship between math and the sounds of strings on

musical instruments.musical instruments.Clipart Credit: Clkr.com Free ClipartClipart Credit: Clkr.com Free Clipart

Pythagoras

Discuss the definition of the Pythagorean Theorem.Discuss the definition of the Pythagorean Theorem.The square of the hypotenuse of a right triangle is equal to the combined squares of the two legs of The square of the hypotenuse of a right triangle is equal to the combined squares of the two legs of

the same triangle.the same triangle.

The Pythagorean TheoremThe Pythagorean Theorem

aa22 + b + b22 = c = c22

hypotenuseleg

leg

a2

b2

c2

Description of objectives. By the end of this video you will Description of objectives. By the end of this video you will be able to:be able to:- Recognize right triangles.- Recognize right triangles.- Determine whether it is appropriate to use the - Determine whether it is appropriate to use the Pythagorean theoremPythagorean theorem- Construct the Pythagorean theorem equation and solve it.- Construct the Pythagorean theorem equation and solve it.- Identify real life situations in which to use the Pythagorean - Identify real life situations in which to use the Pythagorean theorem.theorem.

ObjectivesObjectives

Characteristics of a right triangle:Characteristics of a right triangle:3 sides - leg, leg, hypotenuse3 sides - leg, leg, hypotenuse

one angle is always 90°one angle is always 90°hypotenuse is the longest side and is across from the 90° anglehypotenuse is the longest side and is across from the 90° angle

Right TriangleRight Triangle

leg

leg

hypotenuse

90°

Please take a few seconds and choose which triangle is a right triangle!Please take a few seconds and choose which triangle is a right triangle!

Which triangle is a right Which triangle is a right triangle?triangle?

A. B. C.

Let’s put the Pythagorean theorem to use and put it in an equation! Let’s put the Pythagorean theorem to use and put it in an equation! I will discuss how to set up the equation.I will discuss how to set up the equation.

Equation

ac

b

a2 + b2 = c2

Now it’s your turn to set up an equation using the Pythagorean theorem. I will give you a few Now it’s your turn to set up an equation using the Pythagorean theorem. I will give you a few minutes before I present the proper equation for you to compare to what you wrote.minutes before I present the proper equation for you to compare to what you wrote.

Your turn!Your turn!

3

4

c

32 + 42 = c2

Solve for cSolve for c

Now that you have produced the equation it’s time to solve it.The viewers will be given about 30 seconds to solve the equation before the solving

process begins to enter the screen.

32 + 42 = c2

9 + 16 = c2

9 + 16 = 25√25 = 5

C = 5

32c2

42

Let’s try one Let’s try one more!more!

15

9

a

a2 + 92 = 152

a2 + 81 = 225

a2 + 81 = 225-81 -81

a2 = 144

√144 = 12

a = 12

The viewers will be given the triangle and about 30 seconds to solve the problem. After 30 seconds the steps to solve the problem will begin to enter the screen accompanied by the explanation.

In which real world situation would you use In which real world situation would you use the Pythagorean Theorem?the Pythagorean Theorem?

The viewer will be asked to choose which situation would it be appropriate to use the Pythagorean theorem in.I will briefly discuss the correct answer and the reason.

How far is the fall?How far is the fall?

6

10

a2 + 62 = 102

a2 + 36 = 100 -36 -36

a2 = 64

√a2 = √64

a = 8

a = 8

I will discuss the problem which is to be solve: How far is the fall? The viewers will be given time to solve the problem before the solution appears on the screen

Let’s review!Let’s review!

Right Triangle

ac

b

a2 + b2 = c2

Pythagorean Theorem

I will quickly review what was taught in the video: the right triangle and the Pythagorean Theorem.