## anonymous one year ago Karen 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 6, the length of DB is equal to 2, the length of AE is equal to 7 and the length of EC is equal to 3. She starts with the assumption that segment DE is parallel to segment BC. Which inequality will she use to contradict the assumption?

1. anonymous

6:7 ≠ 2:7 6:8 ≠ 7:10 6:2 ≠ 7:10 6:2 ≠ 3:2

2. anonymous

@Anaise

3. anonymous

@zepupster

4. anonymous

@Zpupster

5. anonymous

@Michele_Laino

6. Michele_Laino

please can you make a drawing of your triangle?

7. anonymous

8. Michele_Laino

we can say that the assumption is a contradicted if and only if there is no proportionality between corresponding segments, or in other words, if the subsequent condition holds: $6:2 \ne 7:3$

9. Michele_Laino

now I apply the componendo property, so I get this: $6:\left( {6 + 2} \right) \ne 7:\left( {7 + 3} \right)$

10. Michele_Laino

so, what is the right option?

11. anonymous

b?

12. anonymous

sorry i got caught up

13. anonymous

@Michele_Laino is b right?

14. Michele_Laino

correct!

15. anonymous

thank you! :)