Question

In the given figure, AD perpendicular BC, then find AB^2+ CD^2​

Answer 1

Answer:

Given :  △ ABC where

AD ⊥ BC

To prove : AB2+CD2 = BD2+AC2

Proof :

Since AC⊥ BD

L ADC=L ADB = 90*

So triangle ADB is a right angle triangle

Using pythagoras theorem

(Hypotenuse)2 = (Height)2+(Base)2

(AB)2=(AD)2+BD2

                                   .......(1)

_______________________________

So, triangle ADC is a right angle triangle

Using pythagoras theorem  

(Hypotenuse)2 = (Height)2+(Base)2

(AC)2=(AD)2+CD2

                                   .......(2)

Doing (1)-(2)

AB2-AC2 = (AD2+BD2) - (AD2+CD2)

AB2-AC2 = AD2+BD2 - AD2-CD2

AB2-AC2 =BD2-CD2

AB2+CD2= BD2+AC2

Hence proved...

hope it helps u..........