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Question

# Prove the following :In fig if ABCD is a trapezium in which AB∥DC∥EF then AEED=BFFC OR Any line parallel sides of a trapezium divides the non-parallel sides proportionally

A
AEED=BFFC
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B
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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=BFFCIn a trapezium ABCD AB∥DC∥EF, WE have to prove, AEED=BFFC Join AC which intersects EF at GProof IN △CAB,GF∥AB ∴FCBF=CGAG ( Using Thales Theorem) ⇒BFFC=AGCG....(ii)(Taking reciprocals) △ADCEG∥DC ∴AEED=AGGC ....(ii)(By Thales Theorem)From (i) and (ii) we get AEED=BFFC

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