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.

In the figure X is any point in the interior of triangle. Point X is j

1.	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» 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)

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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.

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