Question

Three parallel lines l,m and n are intersected by a transversal p at points A,B and C respectively and transversal q at D,E and F respectively . If AB:BC=1:2 , prove that DE:EF=1:2

Answer 1

Join AF which cuts AE at G.In △ACF, BG ∥CFBy Basic Proportionality theorem, A line parallel to one side of a triangle divides the other two sides intoparts of equal proportion.So, ABBC=AGGF = 12−−−−−−−−−−−−−−−(1)In △AFD, GE ∥ADBy Basic proportionality theorem,AGGF=DEEF=12−−−−−−−−−−−−−−−−−−(2)From (1) and (2)ABBC=DEEF=12Hence Proved

Answer 2

Answer:

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