Question

5. Given: In trapezium PQRS,
side PQ || side SR, AR = 5AP,
AS = SAQ then prove that,
you
SR = 5PQ
R
Fig. 1.59​

Answer 1

Given That :

Side PQ || side SR

AR = 5AP

AS = 5 AQ

To Prove : SR = 5PQ

Proof :

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

 厶工リ乇