TOPIC 8: PYTHAGORAS THEOREM ~ MATHEMATICS FORM 2
Pythagoras Theorem
Triangle with a Right angle i.e. 90° has an amazing property. Do you want to know what property is that? Go on, read our notes to see the amazing property of a right angled triangle.
This kind of a Triangle is called Right angled triangle. When triangle is a right angled triangle, squares can be made on each of the three sides. See illustration below:



‘c’ is the Longest side of the Triangle, is called Hypogenous and is the one that forms the biggest square. a and b are the two smaller sides.
Proof of Pythagoras Theorem
The Pythagoras Theorem
Prove the pythagoras theorem
smaller sides is exactly equal to the square of Hypotenuse side (large
side). i.e. a2 + b2 = c2
See the figure below:

The area of a whole square (big square)

But there are 4 triangles and they are equal, so total area =
Both areas must be equal, the area of a big square must be equal to the area of a tilted square plus the area of 4 triangles
Exercise 1
- c if a = 5 and b = 12
- a if b = 8 and c = 12
- b if a = 9 and c = 11
2. A rectangle has base 6 and height 10. What is the length of the diagonal?
3. A square has a diagonal with length 6. What is the length of the sides of the square?
A ladder leans against a wall. If the ladder reaches 8m up the wall and
its foot is 6m from the base of the wall. Find the length of the
ladder.
The Pythagoras Theorem
Prove the Pythagoras theorem
Pythagoras
theorem states that: In a Right Angled Triangle, the sum of squares of
smaller sides is exactly equal to the square of Hypotenuse side (large
side). i.e. a2 + b2 = c2
The area of a whole square (big square)
Second, area of the equal triangles each with bases a and height b:

Both areas must be equal, the area of a big square must be equal to the area of a tilted square plus the area of 4 triangles
Exercise 2
- c if a = 5 and b = 12
- a if b = 8 and c = 12
- b if a = 9 and c = 11
3. A square has a diagonal with length 6. What is the length
Application of Pythagoras Theorem
The Pythagoras Theorem to Solve Daily Life Problems
Apply the Pythagoras theorem to solve daily life problems
in your math class, but what you may fail to realize is that
Pythagoras’s theorem is used often in real life situations.
For example,
calculating the distance of a road, television or smart phone screen
size (usually measured diagonally).
Activity 1
Apply the Pythagoras theorem to solve daily life problems
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