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Question:

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

Solution:

In ΔPOQ, DE||OQ ∴By basic proportionality theorem, PE/EQ = PD/DO (1)
Similarly, In ΔPOR, DF||OR ∴By basic proportionality theorem, PD/DO = PF/FR (2)
∴from (1) and (2), PE/EQ = PF/FR
∴By converse of Basic Proportionality Theorem, EF||QR