Question

State and proove "Pythagoras Theorem " by using the concept of similarity of triangles .​

Answer 1

Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given: ABC is a triangle in which ∠ABC=90  

∘

 

Construction: Draw BD⊥AC.

Proof:

In △ADB and △ABC

∠A=∠A              [Common angle]

∠ADB=∠ABC      [Each 90  

∘

]

△ADB∼△ABC    [A−A Criteria]

So,  

AB

AD

​  

=  

AC

AB

​  

 

Now, AB  

2

=AD×AC             ..........(1)

Similarly,

BC  

2

=CD×AC               ..........(2)

Adding equations (1) and (2) we get,

AB  

2

+BC  

2

=AD×AC+CD×AC

=AC(AD+CD)

=AC×AC

∴AB  

2

+BC  

2

=AC  

2

 [henceproved]