If after reading the other pages and posts, you feel you need a brush-up on Pythagoras’ Theorem, read on.

 We can see in the diagram below that, in the triangle ABC, if a perpendicular is dropped from point A to side a at point D, ABC is divided into 2 smaller triangles which are both similar to ABC.


Consider triangle (i).  Since this triangle is similar to ABC, it follows that:

a÷b  =  b÷x

→  b2  =  ax    …………….(i)

Now consider triangle (ii); by similar argument:

a÷c  =  c÷y

→  c2  =  ay    …………….(ii)

Combining (i) and (ii) we get:

b2  +  c2  =  ax + ay

Þ  a( x + y )  =  b2  +  c2

But  a  =  x + y

→  a2 =  b2  +  c2  This is Pythagoras’ Theorem

 Simple Example


The distance from town A to town B is 48.5Km.

The distance from town B to town C is 38.25Km.

What is the distance from town C to town A?

By Pythagoras,

CA2  =  AB2 + BC2

→ CA2  =  48.52 +  38.252

=  2352.25  +  1463.06

=  3815.31

→  CA     =  √3815.31

=  61.77Km.

Therefore the distance from town C to town A is 61.77Km.

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