Pythagoras discovered that the ancient Egyptians used a 3:4:5 right triangle to build the pyramids. He investigated this further and deduced the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras proved this by drawing squares on each side of right triangles and showing that the areas added up. The Pythagorean theorem has been used since ancient times in architecture, engineering, and more recently in technology like screens.

1. 5
4
3

2. 5
4
3
In Egypt, Pythagoras found out that they were
using measurements with a Right Angled
Triangle with sides of 3, 4, and 5 units
to build the Pyramids.
He decided to investigate this further.

3. Hypotenuse
Pythagoras started with a 90 degree (L-shaped)
Right Triangle. He named the long sloping side
the “Hypotenuse”.

4. 5
4
3
Next he added a Square onto each Triangle Side.

5. 5
4
3
Next he added Grid Lines to measure Areas.

6. C2 = 5 x 5 = 25
A2 = 4 x 4 = 16 5
4
3
B2 = 3 x 3 = 9
He found that the Areas of the two side squares add up
to equal the Area of the long sloping “Hypotenuse” square.
Eg. 16 + 9 = 25

7. 5
4
5 13
3
12
X2
8 10 17
8
6 15
Pythagoras rule works on all Right Angled Triangles

8. c = “Hypotenuse”
Sloping Side
a = Altitude
a2 + b2 = c2
b = Bottom Base
a2 + b2 = c2
a=6 6 10 c = 10
62 + 82 = 102
8 36 + 64 = 100
b=8 100 = 100
This 6,8,10 Right Triangle obeys Pythagoras Rule.

9. Pythagoras Rule has been used since the days of
the Pyramids to the present. Triangular shapes add
strength and rigidity to buildings and bridges.

10. Pythagoras Rule is used in TVs and Projectors, as well as
for Phone and Computer screens in the form of 4:3 and
16:9 viewing aspect ratios. The size of the screen is
measured as the Diagonal of the right triangle.

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