Question

In figure 1.41, if AB||CD||FE then find x and AE

Answer 1

theorems: the ratio of the intercept made on a transversal by three parallel lines is equal to the ratio of the corresponding intercept made on any other transversal by the same parallel lines.
BD/DF =AC /CE
8/4=12/x
x= 12×4 /8
x=6
now, AE =AC+CE
12+x
12+6
AE=18
thank you

Answer 2

Solution :

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Intercept Theorem :

If there are three or more parallel

straight lines and the intercepts made

by them on any transversal are equal

then the corresponding intercepts

on any other transversal are also

equal .
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Here ,

AB // CD // EF ,

CE/AC = DF/DB

=> x/12 = 4/8

=> x = ( 4 × 12 )/8

=> x = 6

AE = AC + CE

=> AE = 12 + 6 = 18

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