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Question

l,m,n are parallel lines. If p intersects them at A,B,C and q at D,E,F, then

A
AB=DE and BC=EF always
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B
At least one of the pairs AB,DE and BC,EF are necessarily equal
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C
At least one of the pairs AB,BC and DE,EF are necessarily equal
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D
ABBC=DEEF
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Solution

The correct option is B ABBC=DEEF
Given: l||m||n and we have two transversal p and q, there cut A,B,C and D,E,F.
By Construction, we take point O at the intersection of both transversed line p and q.
and FXOCandCYOF.Join AF,BF,DC and EC.
Since,FXOC,SoFXis height ofOCF&BCF.
ar(OCF)=12×OC×FX
ar(BCF)=12×BC×FX
ar(BCF)ar(OCF)=BCOC(1)
Similarily,Since CYOF,So CY is height ofOCF&ECF,
ar(ECF)ar(OCF)=EFOF(2)
ButBCFandECF are on the same base CF b/w same parallel straight lines BC& CF {m||n}
BCF=ECF(3)
BCOC=EFOF(A)
Since,FXOC,FX is height ofOCF&ACF
ar(OCF)=12×OC×FX
ar(ACF)=12×AC×FX
ar(ACF)ar(OCF)=ACOC=AB+BCOC(4)
Since,CYOF,SoCYisheightofOCF&DCF.
ar(DCF)ar(OCF)=DE+EFOF
ButACF&DCF are on same base CF and b/w same parallel straight line,
Since,ADandCF{AD||CFasl||n}
ACF=DCF(6)
ABOC+BCOC=DEOF+EFOF
ABOC=DEOF(B){EFOF=BCOC}
ABOCBCOC=DEOFEFOF
ABBC=DEEF

1013391_927026_ans_cbf1f0706a084e72a539d5d2ae158bcd.png

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