http://www.geom.uiuc.edu/~demo5337/Group3/hist.html

*Pythagoras was born in Greece, and he did a lot of traveling to Egypt to learn things and mathematics. *In his early years, he was not known much. However, Pythagoras gained his famous status by founding a group; it includes "Brotherhood of Pythagoreans", which is focused on a study of mathematics.*Even though Pythagoras is credited with discovering the famous theorem, it is not possible to say if he is the actual author.

You are going to learn:

What are the qualifications of the triangle to be right.

How to apply the Pythagorean ' formula on the three legs.

How to apply the equation for triangles in graphics and

everyday life by using Pythagorean Theorem.

1-

2-

3-

There are many kinds of triangles such as Equilateral Triangle, IsoscelesTriangle, and right triangle. We are going to explain the right triangle in this

lesson.

Kinds of Triangles:

3

4

3

Right Triangle

IsoscelesTriangle

3

4

3

35

4

Equilateral Triangle

1- A right triangle has 90° angle on A-B corner. 2- The hypotenuse C should be the largest side in the right triangle.

3

5

4

Hypotenuse

A

B C

The qualifications of a Right Triangle

90°

These legs are marked with an ‘A‘, ‘B‘, while the hypotenuse is marked with a ‘C‘

In this case, the formula is A2 + B2 = C2. The sum of the squares of the two lengths of legs (A+B) equals the

square of the length of the Hypotenuse (C)

3

5

4

Hypotenuse

A

B C

Explain the Pythagorean' Theorem

90°

The Pythagorean theorems' formula is A2 + B2 = C2

42 + 32 = c2

4x4 + 3x3 = c2

16 + 9 = c2

√ 25 = c2

√ 25= 5

3

?

4

Hypotenuse

A

B C

Finding the Hypotenuse

90°

???

8

Find the length of leg C in the

triangle on the left.

A

B

C

Practice Problem (1)!!

6

90°

First check these points then start:1- Right-angled triangle { }2- The hypotenuse C is the largest side{ }

???

8

Find the length of leg C in the

triangle on the left.

A

B

C

Practice Problem (1-A)!!

6

90°

First check these points then start:1- Right-angled triangle { }2- The hypotenuse C is the largest side{ }

10

8

A2 + B2 = C2

82 + 62 = C2

8x8 + 6x6 = C2

64+ 36 = C2

√ 100 = C2

√ 100 = 102

C2 = 10

A

B

C

Answer the Practice(1-B)

6

90°

The answer is C = 10

???

72

Find the length of leg C in this

triangle.

AB

C

Practice Problem(2)!!

21

90°

First check these points then start:1- Right-angled triangle { }2- The hypotenuse C is the largest side{ }

???

72

Find the length of leg C in this

triangle.

AB

C

Practice Problem(2-A)!!

21

90°

First check these points then start:1- Right-angled triangle { }2- The hypotenuse C is the largest side{ }

75

72A

B

C

Answer the Practice(2-B)

21

90°

A2 + B2 = C2

722 + 212 = C2

72x72 + 21x21 = C2

5184+ 441 = C2

√ 5625 = C2

√ 5625 = 752

C2 = 75

The answer is C = 75

How to Apply Pythagoras' Theorem in the Daily Life

Computer

By knowing the two lengths between this man and the highest point (4 miles) and the lowest point (3 miles), we can measure how tall it is.

How to use Pythagoras' theorem to measure the tall of house or tree?

4 miles

3 miles

??

Finding the Right Size for Computer: If you want to get a new computer, and you have for example 22 inch as a size of the holder. By using Pythagoras' Theorem, you are going to measure the height and width of the new computer screen before buying it to find out whether the diagonal length(22) inch is the a perfect size to fit in your holder or not!

How to use Pythagoras' theorem to measure the diagonal length of computer?

Computer

22

??

??

Review of Pythagoras' theorem

Review: The qualifications of Right Triangle: It has to be 90° + the hypotenuse should be the largest .

The Pythagorean ' theorem:

It is : A2 + B2 = C2

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2-

The End

Thank you