An important question from similarity chapter in which we have been asked to Prove BM/MC = AL/LQ, if AB || CR and LM || QR
ML Aggarwal Avichal Publication, Class 10, Similarity, question no 9a
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In ΔMBA & ΔMCR
∠MBA=∠MCR{ given AB∣∣CR and we take BC as transversal line}
∠AMB=∠RMC { vertically opposite angle}
So,△MBA∼△MCR{ By AA rule}
ThenBM/MC=AM/MR −(i)
and In△ARQ,
given LM∣∣QR,
so from B.P.T we got:
AM/MR=AL/LQ −(ii)
⟹BM/MC=AL/LQ