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Class 9-10, JEE & NEET
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In three line segments OA, OB and OC points L, M, N respectively are so chosen that LM || AB and MN || BC but neither of L, M, N nor of A, B, C are collinear. Show that LN || AC.
In ∆OAB, since LM∥AB, thenOLLA = OMMB By BPT ........1In ∆OBC, since MN∥BC, then OMMB = ONNC By BPT ⇒ ONNC = OMMB .........2from 1 and 2, we get OLLA = ONNC