Question

In which of the following drawings is DE parallel to AC?​

Answer 1

C

Explanation:

Answer 2

Option (C)

Explanation:

In this question we will use the property " similarity of the triangles".

If DE and AC are parallel two triangles BED and BCA will be similar, corresponding sides of the triangles will be proportional.

`\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}`

Option (A).

`\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}`

`(22+12)/(12)=(14+26)/(14)`

`(34)/(12)=(40)/(14)`

`(17)/(6)=(20)/(7)`

But
`(17)/(6)\\eq (20)/(7)`

Therefore, given triangles are not similar.

AC and DE are not parallel.

Option (B).

`\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}`

`(25)/(25-7)=(21+9)/(21)`

`(25)/(18)=(30)/(21)`

`(25)/(18)=(10)/(7)`

But
`(25)/(18)\\eq (10)/(7)`

Therefore, AC and DE are not parallel.

Option (C).

`\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}`

`(22.5+15)/(15)=(40)/(40-24)`

`(37.5)/(15)=(40)/(16)`

2.5 = 2.5

Therefore, AC║DE.

Option (D).

`\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}`

`(17.5+5)/(17.5)=(20.4+6)/(20.4)`

`(22.5)/(17.5)=(26.4)/(20.4)`

`(9)/(7)=(22)/(17)`

But
`(9)/(7)\\eq (22)/(17)`

Therefore, AC and DE are not parallel.

Option (C) will be the answer.