Question

Hola!Gimme the Pythagorus theorem and the converse of it

Thenks^_^
~@Nikki ❤

Answer 1

I hope this theorem may help you

Answer 2

Answer:

Proof of Pythagoras Theorem-

To Prove- AC2=AB2+BC2</p >

Proof for Pythagoras Theorem

For this we drop a perpendicular BD onto the side AC

We know, △ADB∼△ABC

Therefore, ADAB=ABAC (Condition for similarity)

Or, AB2=AD×AC……..(1)

Also, △BDC∼△ABC

Therefore, CDBC=BCAC (Condition for similarity)

Or, BC2=CD×AC……..(2)

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

AB2+BC2=AD×AC+CD×AC

AB2+BC2=AC(AD+CD)

Since, AD + CD = AC

Therefore, AC2=AB2+BC2

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 Converse of this theorm :

construct another triangle as follows given in the attachment  :

     EF = BC = a

ÐF is a right angle.

  FD = CA = b

  In  DDEF,

  By Pythagoras Theorem,

         ……..(2)

  By (1), the given,

         

  Theorefore,                 AB = DE

  But by construction,       BC = EF

  and                                 CA = FD

                            D ABC @ D DEF (S.S.S.)

Hence proved !!