LM PARALLEL TO CB AND LN PARALLEL TO CD if AM/MB=AL/LC WHAT IS EQUAL TO AN/ND
Answers
It is given that LM∥CB and LN∥CD
From the diagram we see that in ΔABC,
It is given that LM∥CB
∴ By applying proportionality theorem we get
AMMB=ALLC....(1)
In a similar way, in ΔADC we get-
It is also mentioned in the question that LN∥CD
Again, by applying proportionality theorem we get-
ANND=ALLC....(2)
From equations (1)and (2) it is clear that since both AMMBand ANND equals to ALLC
Therefore, AMMB=ANND
Now, by applying the principle of invertendo we get-
MBAM=NDAN
Now by adding 1on both the sides we get,
MBAM+1=NDAN+1
Taking LCM on both sides we get,
MB+AMAM=ND+ANAN
From the given diagram shows that MB + AM = ABand ND + AN = ADwe get,
ABAM=ADAN
Again, by applying the principle of invertendo we get-
AMAB=ANAD
Answer:
Solution
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In △ABC,
LM∥BC
∴ By proportionality theorem,
AB
AM
=
AC
AL
............(1)
Similarly,
In △ADC,
LN∥CD
∴ By proportionality theorem,
AD
AN
=
AC
AL
............(2)
∴ from (1) and (2),
AB
AM
=
AD
AN