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Arithmetic Problem Solving
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Read up about the History of the man who was the first to proof this Theorem:
History of Pythagoras.pdf
Want to see more portraits of him? Go to:
So, how did he discover the theorem?
Well, legend has it that he got his inspiration from looking at floor tiles~
(yup, just like how Decartes got his inspiration of the Coordinate System by looking at a fly~)
Here is one such tile:
Ok, probably not...
Got it? Hmm......
Ok, to get the idea, go to the next section...
Concept of Pythagoras Theorem
So, what exactly is this theorem that Pythagoras discovered?
Basically, the theorem states that
, the square of the length of the longest side (called the hypotenuse) is equal to the sum of squares of the length of the other 2 sides".
Important points to note:
(1) The triangle MUST have an angle that is 90 deg.
(2) a^2 in the above equation always refers to the LONGEST side.
Proofs of the theorem:
To show that the theorem is true, think of it in this way:
In the above diagram, notice that the sides of the white triangle are also the lengths of 3 different squares. We can make use of the lengths to define the area of the 3 squares as a^2, b^2 and c^2.
To show that Pythagoras Theorem is true, all we need to do is to prove that the area of a = area of b + area of c.
Meaning, if we can show that a^2 = b^2 + c^2, we have proven pythagoras theorem.
There are many different ways to make the 2 smaller squares fit into the big square. Go to this website and try the interactive applets for yourself:
To start, click on "Define" to show the red dots. Then move the pieces by clicking onto the red dot.
To reset, click on "Init".
Here's an animated version:
While there are many many proofs of Pythagoras Theorem, some basic and some advanced, understanding them all is beyond your scope. Still, to see 84 of them, go to:
Fun Trival: One American President discovered a proof of Pythagoras Theorem. Do you know who he is?
"In 1876, Garfield discovered a
of the Pythagorean Theorem using a trapezoid while serving as a member of the House of Representatives.]"
are integers that form the three sides of a right triangle.
(3, 4, 5) --> 5^2 = 3^2 + 4^2
(5, 12, 13) --> 13^2 = 5^2 + 12^2
There are more of them! Can you think of some yourself?
There is a rule to generate these triplets. Can you find it? You may share your findings on the
Examples on how to solve problems using Pythagoras Theorem:
1) You have allocated a space of 48 inches wide by 35 inches high for a TV. Will a 65-inch TV fit into the space? [65-inch refers to the length of the diagonal of the TV)
Solution: Use Pythagoras Theorem to find the length of the diagonal of the space you have.
You have only 60 inches available. Hence, a 65-inch TV will not fit into the space.
2) In the diagram below, find the lengths of AB and CD.
To find AB:
To find CD:
Chapter 7, Ex
(Do in Exercise Book)
Attempt the ConcepTest by
Sunday 25/4 6 pm
Link to google form for ConcepTest:
Diagram for Q2:
The solution to the above problem is given in the following slides, as shared by one of your classmates in the JiTT exercise:
Worksheets and Solutions:
Pythagoras Theorem Worksheet.pdf
Q1 - Q6 are basic questions.Q7 - Q14 are more challenging.
Solution for Q1 - Q6
Pythagoras Theorem Q1-6 Solutions.pdf
Solution for Q7 - Q14:
Pythagoras Theorem Q7-14 Solutions.pdf
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