Question

​PQRS is a quad. A line through S parallel to PR meets QR produced in X.Show that ar(PQRS) =ar(PXQ).

Answer 1

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Given: PQRS is a quadrilateral. ​SX | | PR 
To prove: ar(PQRS) = ar(PXQ)
Proof
Consider ​ΔPSX and ​ΔSRX. They lie on same base SX and between same parallels ​SX | | PR
Therefore, 
ar(PSX) =  ar(SRX) → (i)
Subtracting ar(SYX) from both sides of Eqn (i) we get 
ar(PSX) - ar(SYX)=  ar(SRX) - ar(SYX)​
ar(PSY) = ar(XYR) → (ii)
Adding ar(PYRQ) to both sides of Eqn (ii) we get 
ar(PSY) + ar(PYRQ) = ar(XYR) ​+ ar(PYRQ)
ar (PQRS) = ar (PXQ)
Hence Proved