Question

Adrian 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 5, the length of DB is equal to 3, the length of AE is equal to 6 and the length of EC is equal to 4.

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

Which inequality will he use to contradict the assumption?

5:3 ≠ 6:10
5:8 ≠ 6:4
5:8 ≠ 6:10
5:3 ≠ 5:6

Answer 1

5:8 ≠ 6:10

Explanation:

yes

Answer 2

If we start with the assumption that segment DE is parallel to segment BC, then we the similarity condition that:
triangle ABC is similar to triangle ADE
For this to be true, the ratio corresponding sides of the two triangles must be equal. So:
5/8 =? 6/10
But
5/8 =/= 6/10

So, DE is not parallel to BC