History of Pythagoras
*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.
http://www.geom.uiuc.edu/~demo5337/Group3/hist.html
The Objectives of This Lesson
You are going to learn:
123-
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.
Kinds of Triangles:
3
3
Equilateral
Triangle
5
3
Right Triangle
3
4
4
4
Isosceles
Triangle
3
There are many kinds of triangles such as Equilateral Triangle, Isosceles
Triangle, and right triangle. We are going to explain the right triangle in this
lesson.
The qualifications of a Right Triangle
Hypotenuse
5
B
C
3
90°
A 4
1- A right triangle has 90° angle on A-B corner.
2- The hypotenuse C should be the largest side in the right triangle.
Explain the Pythagorean' Theorem
Hypotenuse
5
B
3
C
90°
A 4
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)
Finding the Hypotenuse
Hypotenuse
?
B
C
3
90°
A 4
The Pythagorean theorems' formula is
A2 + B2 = C2
42 + 32 = c2
4x4 + 3x3 = c2
16 + 9 = c2
√ 25 = c2
√ 25= 5
Practice Problem (1)!!
Find the length of
leg C in the
triangle on the
left.
C ???
B
6
First check these points then start:
1- Right-angled triangle {
}
2- The hypotenuse C is the largest side{
A8
}
90°
Practice Problem (1-A)!!
Find the length of
leg C in the
triangle on the
left.
C ???
B
6
First check these points then start:
1- Right-angled triangle {
}
2- The hypotenuse C is the largest side{
A8
}
90°
Answer the Practice(1-B)
A2 + B 2 = C2
82 + 62 = C2
8x8 + 6x6 = C2
64+ 36 = C2
√ 100 = C2
√ 100 = 102
C2 = 10
C 10
B
6
90°
A8
The answer is C = 10
Find the length of
leg C in this
triangle.
Practice Problem(2)!!
C
???
First check these points then start:
1- Right-angled triangle {
}
2- The hypotenuse C is the largest side{
}
B
A
21
72
90°
Find the length of
leg C in this
triangle.
Practice Problem(2-A)!!
C
???
First check these points then start:
1- Right-angled triangle {
}
2- The hypotenuse C is the largest side{
}
B
A
21
72
90°
A2 + B 2 = C2
722 + 212 = C2
72x72 + 21x21 = C2
5184+ 441 = C2
√ 5625 = C2
√ 5625 = 752
C2 = 75
Answer the Practice(2-B)
75
C
B
21
A
72
The answer is C = 75
90°
How to Apply Pythagoras' Theorem in the Daily Life
Computer
How to use Pythagoras' theorem to measure the tall of
house or tree?
4
miles
??
3 miles
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
diagonal length of computer?
??
??
Computer
22
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!
Review of Pythagoras' theorem
Review:
1-
2-
The qualifications of Right Triangle:
It has to be 90° + the hypotenuse should be the largest .
The Pythagorean ' theorem:
It is : A2 + B2 = C2
Thank you
The End