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In three line segments OA, OB and OC points L, M, N

Question:

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.

Solution:

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    

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