In the figure, If ML || BC and NL|| DC.
Then prove that AM/AB = AN/AD
Answers
STEP BY STEP EXPLAINATION ÷
In triangle ABC. ML|| CB
=AM/BM =AL/ CL eq-1) by BPT
THEOREM
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NOW. , In triangle ADC LN || D C
=AN/DN. = AL/CL. Eq -2) by BPT
THEOREM
===================================
From comparing eq 1 and eq 2 we get
》AM/BM = AN/DN
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~
{NOW WE ADD 1 ON BOTH SIDE }
》》 AM/BM +1 = AN/DN + 1
~》 AM / BM +AM. = AN / BM +AM
》》 AM / AB. = AN / AD
HENCE PROVED
In ∆ ABC,
ML || BC _ _ _ _ ∵ Given
AM/MB = AL/LC _ _ _ _ ∵ BPT _ _ (I)
In ∆ ADC,
NL || DC _ _ _ __ _∵ Given
AN/ND = AL/LC _ _ _ _ ∵ BPT _ _ (II)
From (I) & (II)
AM/MB = AN/ND
MB/AM = ND/AN _ _ _ ∵ By invertendo
Property
MB + AM/AM = ND + AN/AN
∵ By Componendo Property
AB/AM = AD/AN _ _ _ ∵ A-M-B & A-N-D
AM/AB= AN/AD _ _ ∵ By Invertendo prop.
Hence proved !
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