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Question

In figure, ABCD is a trapezium with AB||DC. If AED is similar to BEC, which of the following is true?



A
EA = EB
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B
EA = AD
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C
AD = BC
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D
BC = EB
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Solution

The correct options are
A EA = EB
C AD = BC

In EDC and EBA, we have

1 = 2       
3 = 4   
( alternate angles are equal)

and CED = AEB       
( vertically opposite angles are equal)

EDCEBA (By AA similarity criterion)

EDEB = ECEA       

EDEC = EBEA    ......(i)

It is given that AED BEC

EDEC = EAEB = ADBC    ......(ii)

From (i) and (ii), we get

EBEA = EAEB

(EB)2 = (EA)2

EB=EA

On substituting EB = EA in (ii), we get

EAEA =ADBC

ADBC = 1

AD=BC


Mathematics

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