THE PYTHAGORAS THEOREM

BY: DILSHAN 8B1

WHO IS PYTHAGORAS?Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece, and did much traveling through Egypt, learning, among other things, mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group, the Brotherhood of Pythagoreans, which was devoted to the study of mathematics.

The group was almost cult-like in that it had symbols, rituals and prayers. In addition, Pythagoras believed that "Number rules the universe,“ and the Pythagoreans gave numerical values to many objects and ideas. These numerical values, in turn, were endowed with mystical and spiritual qualities.

WHAT IS PYTHAGORAS FAMOUS THEORY?

Over 2000 years ago, there was an amazing discovery about triangles!When a triangle has a right angle and squares are made on each of the three sides, then the biggest square has the exact same area as the other two squares put together!

It is called the `Pythagoras Theorem’ and can be written down using this simple equation:a(2)+b(2)=c(2)

Note:• c is the longest side of the triangle, also called

`hypotenuse’.• a and b are the other two sides.

HOW DOES THE PYTHAGORAS THEOREM HELP US IN OUR EVERYDAY LIFE?It is perhaps the most powerful mathematical equation used in the building trade.

Using it, drawings can be enlarged, foundations can be laid out and perfectly square angles can be calculated. It can be used by everyone from surveyors who want to find out how tall a mountain is to astronomers who want to calculate the distance to the sun or the circumferences of the moon. Carpenters can use it to keep their work square. Draftsmen use it to make sure their architectural drawings are accurate.

It's a very powerful equation.

TIME FOR THE QUESTIONS!

To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?

SOLUTION:• First of all, the question is telling you to find the hypotenuse, in other words.• So, you have to square 34 and 41 then add the results together.• Whatever answer you get, you then have to square root it.• Finally, you got your answer. And remember to round it to the nearest meter when you have to.

[5 MARKS]Answer: 22m

Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across.What is the height of his dog house, in feet, at its tallest point?

SOLUTION:• Firstly, you have to half the original base of the house, which is 6’. So you can

use this 3’ as the half base of the house.• Then, just square 3 and 5 then whatever results you get, you have to minus it

this time.• Afterwards, the answer you get, you have to then square root it.• Finally, you got your answer! Remember to write feet next to your answer.

ANSWER: 4feet [5 MARKS]

THAT’S ALL THE QUESTIONS!

TIME FOR THE QUIZ!

Q1. THE PYTHAGORAS THEOREM IS A RELATIONSHIP BETWEEN THE LENGTHS OF THE SIDES OF WHAT KIND OF TRIANGLE?

1. ISOSCELES TRIANGLE

2. RIGHT ANGLE TRIANGLE

3. EQUILATERAL TRIANGLE

4. SCALENE TRIANGLE

Q2. WHAT IS THE LENGTH OF THE HYPOTENUSE OF THE RIGHT ANGLE TRIANGLE SHOWN?

1.9

2.12

3.15

Q3. WHICH RELATIONSHIP DESCRIBES THE PYTHAGORAS THEOREM FOR THE SIDES OF THE TRIANGLE?

1. A(2)+B(2)=C

2. B(2)+C(2)=A(2)

3. A(2)+B(2)=C(2)

4. C(2)+A(2)=B(2)

Q4. IF THE LENGTH OF THE LEGS OF A RIGHT ANGLE TRIANGLE ARE 7 AND 24 FEET, WHAT IS THE LENGTH IN FEET OF THE HYPOTENUSE?

1. 25

2. 27

3. 30

4. 34

THAT’S ALL FROM THE QUIZ!

THANKS FOR WATCHING MY POWERPOINT ABOUT THIS

AMAZING THEORY AND I HOPE YOU ALL LEARNT SOMETHING

FASCINATING TODAY!