Question

In trapezium PQRS side PQ parrellel side SR AR =5AP,AS=5AQ, then prove that SR = 5PQ

Answer 1

Given That :

Side PQ || side SR

AR = 5AP

AS = 5 AQ

To Prove : SR = 5PQ

Proof :

In Figure  ( Check Attachment )

We have PQ || RS

          angle PQA = angle ASR  ( Vertically Opposite Angles )

          angle QPA = angle ARS  ( Alternate Interior Angles)

          angle PAQ = angle SAR  ( Alternate Interior Angles)

Thus by AAA Similarity Theorem

Triangle APQ  ~   Triangle ARS

=> AP  = PQ  =  AQ

  ___   ___     ____

   AR     SR       AS

Given : AR = 5AP

=> AP =  PQ

   ___    __

   5AP   SR

=> 1  =  PQ

 ___   ____

    5    SR

=> SR = 5PQ

Hence Proved.

Answer 2

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