Question

Yana is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below:

A triangle ABC is shown. D is a point on side AB and E is a point on side AC. Points D and E are joined using a straight line. The length of AD is equal to 4, the length of DB is equal to 5, the length of AE is equal to 6 and the length of EC is equal to 7.

She starts with the assumption that segment DE is parallel to segment BC.

Which inequality will she use to contradict the assumption?

4:9 ≠ 6:13
4:9 ≠ 6:7
4:13 ≠ 6:9
4:5 ≠ 6:13

Answer 1

4:9 ≠ 6:13

Explanation:

Given,

In triangle ABC,

D ∈ AB, E ∈ AC,

Also, AD = 4 unit, DB = 5 unit, AE = 6 unit, EC = 7 units,

Suppose,

DE ║ BC,

`\because (AD)/(AB)=(AD)/(AD + DB)=(4)/(9)`

`(AE)/(AC)=(AE)/(AE+EC)=(6)/(6+7)=(6)/(13)`

`\implies (AD)/(AB)\\eq (AE)/(AC)`

Because,

`(4)/(9)\\eq (6)/(13)`

Which is a contradiction. ( if a line joining two points of two sides of a triangle is parallel to third sides then the resultant triangles have proportional corresponding sides )

Hence, DE is not parallel to segment BC.

Answer 2

4:9 ≠ 6:13

Explanation:

The ratios of corresponding segments will be equal if DE || BC. Yana can compare AD:AB versus AE:AC. She will find they're not equal, as expressed by ...

4 : 9 ≠ 6 : 13