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Question

Prove the following :
In fig if ABCD is a trapezium in which ABDCEF then AEED=BFFC OR Any line parallel sides of a trapezium divides the non-parallel sides proportionally
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A
AEED=BFFC
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B
AEAD=BFFC
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C
AEED=BFBC
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D
None of these
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Solution

The correct option is D AEED=BFFC
In a trapezium ABCD ABDCEF, WE have to prove, AEED=BFFC Join AC which intersects EF at G
Proof IN CAB,GFAB
FCBF=CGAG ( Using Thales Theorem)
BFFC=AGCG....(ii)
(Taking reciprocals)
ADCEGDC
AEED=AGGC ....(ii)(By Thales Theorem)
From (i) and (ii) we get AEED=BFFC

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