Question

P, Q, R and S are points of the sides AB, BC, CD and DA respectively of a parallelogram
ABCD such that AP =CQ and AS = CR. If QR = 2.5 cm, what is the length of PS ? Is it also
true that PR = QS ? What type of a quadrilateral is PQRS.
plz give me the answer

Answer 1

Answer:

From given information we form our diagram , As :

Here We join PQ , QR , RS and PS .

In ∆ APS and ∆CQR

AP = CQ ( Given )

AS = CR ( Given )

∠SAP = ∠ RCQ ( As we know opposite angles of parallelogram are equal in length )

Hence

∆ APS ≅ ∆CQR ( By SAS rule )

So,

PS = QR ( By CPCT )

SO,

PS = 2.5 cm ( As given QR = 2.5 cm ) ( Ans )

And from this information we can't say PR = QS , SO recheck your question.

Answer 2

Answer:

Here We join PQ  , QR  , RS and PS  .

In Δ∆ APS and Δ∆CQR

AP  =  CQ                                       ( Given )

AS  =  CR                                        ( Given )

∠∠SAP   =  ∠∠ RCQ                 (  As we know opposite angles of parallelogram are equal in length )

Hence

Δ∆ APS ≅≅ Δ∆CQR                ( By SAS rule )

So,

PS  =  QR                                           ( By CPCT )

SO,

PS  =  2.5 cm                                      ( As given QR  = 2.5 cm )                                            ( Ans )

Step-by-step explanation: