Question

Please. Can anyone help me.

Answer 1

correct option is A:
`(4)/(10) \\eq (6)/(14)`

Explanation:

If the segment DE was parallel to the segment BC, we could use the Thales' theorem, where the ratio of one segment created in one side of the triangle over the whole side is the same ratio of one segment created in the other side over the whole side:

`(AD)/(AB) = (AE)/(AC)`

Using the values given (AD = 4, AB = 6+4=10, AE = 6, AC = 8+6=14), we would have:

`(4)/(10) = (6)/(14)`

`4*14=6*10`

`56=60`

This sentence is false, therefore the segments DE and BC are not parallel.

The inequation to prove this is the first one we used, using the "not equal" symbol:

`(4)/(10) \\eq (6)/(14)`

So the correct option is: A