CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

In figure, ABCD is a trapezium with AB||DC, If AED is similar to BEC, prove that AD = BC


Solution

In EDC and EBA, we have

1 = 2       [alternate angles]

3 = 4       [alternate angles]

and, CED = AEB       [vertically opposite angles]

EDC ~ EBA

EDEB = ECEA

EDEB = ECEA               ......(i)

It is given that AED ~ BEC

EDEC = EAEB = ADBC

From (i) and (ii), we get

EBEA = EAEB

(EB)2 = (EA)2

EB=EA

Substituting EB = EA in (ii), we get

EAEA =ADBC

ADBC = 1

AD=BC

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More...


People also searched for
View More...



footer-image