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Solution :

Given : ∆PQR, DE ∥ OQ; DF ∥ OR

R.T.P : EF ∥ QR

Proof :

In ∆POQ;

.....(1)

[∵ ED ∥ QO, Basic proportionality theorem]

In ∆POR;

.....(2) [∵ DF ∥ OR, Basic Proportionality Theorem]

From (1) and (2),

Thus the line

divides the two sides PQ and PR of ∆PQR in the same ratio.

Hence, EF ∥ QR. [∵ Converse of Basic proportionality theorem]

(Q22) In the given figure, DE ∥ OQ and DF ∥ OR. Show that EF ∥ QR.