In parallelogram ABCD, a line through A intersects BD at L, CD at M and BC extended at N. Prove that (L * D ^ 2)/(L * B ^ 2) = (LM)/(LN)
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Step-by-step explanation:
In △BMC and △EMD
∠BMC=∠EMD [Vertically opposite]
MC=DM [Given]
∠BCM=∠EDM [Alternate angles]
∴△BMC≅△EMD [By ASA]
Hence, BC=DE [By CPCT] →(1)
AE=AD+DE=BC+BC=2BC →(2)
Now, △BLC∼△ELA (AA Similarly)
EL /BL = AE /BC [By CPCT] \
EL /BL = 2BC /BC
EL /BL = 2 /1
EL=2BL
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