Question

For which segment lengths is AC¯¯¯¯¯ parallel to DE¯¯¯¯¯ ?

Select Parallel or Not parallel for each set of given information.


Segment lengths Parallel Not parallel


AD = 2, DB = 4, CE = 3, EB = 6



AD = 2, DB = 3, CE = 6, EB = 9



AD = 2, DB = 5, CE = 4, EB = 7

Answer 1

I just took the test, this is the only question i got wrong.

#1-Parallel.

#2-Parallel

#3-Not parallel

Answer 2

Explanation:

By triangle theorem for similarity we have

AC||DE if and only if

the ratios

`(AD)/(BD)=(CE)/(EB)`

Option I:

Here we find the ratios are equal to 1/2

Hence parallel

OPtion 2:

Here we get both ratios equal to 2/3 Hence parallel

Option 3:

Here we get I ratio =2/5 and II ratio =4/7

Since the two are not equal we get not parallel