**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.

^{0}.

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

**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. a

^{2}+ b

^{2 }= c

^{2}

**a**

^{2}+ b^{2}= c^{2}See the figure below:

**The area of a whole square **(big square)

**First**, area of a smaller square (tilted) = c

^{2}

**Second**, area of the equal triangles each with bases a and height b:

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**

^{2}+ 2ab

^{2}+2ab + b

^{2}= c

^{2}+ 2ab

**a**

^{2}+ b^{2}= c^{2}Hence the result!**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. a^{2} + b^{2 }= c^{2}

**a**

^{2}+ b^{2}= c^{2}**The area of a whole square **(big square)

**First**, area of a smaller square (tilted) = c

^{2}

**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**

^{2}+ 2ab

^{2}+2ab + b

^{2}= c

^{2}+ 2ab

**a**

^{2}+ b^{2}= c^{2}Hence the result!**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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