Question

prove that in a right angled triangle square on the hypoteneoue is equal to sum of the square of the other two sides​

Answer 1

Answer:

Pythagoras theorem can proof that

Answer 2

Answer:

Here ye go

Step-by-step explanation:

Given:- A right triangle ABC right angled at B.

To prove:- AC  

2

=AB  

2

+BC  

2

 

Construction:- Draw BD⊥AC

Proof:-

In △ABC and △ABD

∠ABC=∠ADB(Each 90°)

∠A=∠A(Common)

∴△ABC∼△ABD(By AA)

AC

AB

​  

=  

AB

AD

​  

(∵Sides of similar triangles are proportional)

⇒AB  

2

=AD⋅AC.....(1)

Similarly, in △ABC and △BCD

∠ABC=∠BDC(Each 90°)

∠C=∠C(Common)

∴△ABC∼△BCD(By AA)

∴  

BC

DC

​  

=  

AC

BC

​  

 

⇒BC  

2

=DC⋅AC.....(2)

Adding equation (1)&(2), we have

AB  

2

+BC  

2

=AD⋅AC+DC.AC

⇒AB  

2

+BC  

2

=AC(AD+DC)

⇒AB  

2

+BC  

2

=AC  

2

 

Hence proved.