Question

in trapezium PQRS side PQll side SR AR=5
​

Answer 1

Answer:

Given That :

Side PQ || side SR

AR = 5AP

AS = 5 AQ

To Prove : SR = 5PQ

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.

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