Question

In the figure, If ML || BC and NL|| DC.
Then prove that AM/AB = AN/AD​

Answer 1

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

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From comparing eq 1 and eq 2 we get

》AM/BM = AN/DN

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{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

Answer 2

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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