Question

In the figure X is any point in the interior of triangle. Point X is joined to vertices of triangle. Seg `PQ||` set DE, set `QR||` set EF. Fill in the blanks to prove that set `PR||` seg DF.

Answer 1

In `DeltaXDE`, `PQ||DE` .....(Given)
`:.(XP)/(PD)=(XQ)/(QE)`..........`(1)`........(Basic proportionality theorem)
In `DeltaXEF`, `QR||EF`........(Given)
`:.(XQ)/(QE)=(XR)/(RF)`..........`(2)`........(Basic proportionality theorem)
`:.(XP)/(PD)=(XR)/(RF)`.....[From `(1)` and `(2)`]
`:.` seg `PR||` seg `DF`.......(Converse of basic proportionality theorem)