Question

In figure DE || OQ and DF || OR. Show that EF||QR.

Answer 1

In figure , DE||OQ nad DF || OR, then by basic proportionality theorem,
In ` trianglePQO` we have `(PE)/(EQ)= (PD)/(DO)`
and in `trianglePOR`,
`(PF)/(FR)= (PD)/(DO)`
From equations (1) and (2) , ` (PE)/(EQ) = (PF)/(FR)`
Now , in `trianglePQR` we have proved that
`(PE)/(EQ) = (PF)/(FR)`
` Rightarrow " " EF || QR`
( by converse of basic proportionality theorem) .