1.

`P Q R S`is a parallelogram. `P X`and QY are respectively, the perpendiculars from `P`and `Q`to `S R`and `R S`produced. Prove that `P X=Q Ydot`

Answer» PS=QR( opposite sides of parallelogram are equal)
`/_PSR+/_QRS=180^@`
`/_PSR=180^@-/_QRS-(1)`
`/_2+/_QRS=180^@`
`/_2=180^@-/_QRS-(2)`
`/_2=/_PSR=/_1`
`In /_PYS` and `/_QRY`
PS=QR
`/_1=/_2`
`/_PXS=/_PYR`
`/_PXS cong /_BRY(A AS)`
PX=QY.


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