Question

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?

Answer 1

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

Answer 2

@Anaise

Answer 3

@zepupster

Answer 4

@Zpupster

Answer 5

@Michele_Laino

Answer 6

please can you make a drawing of your triangle?

Answer 7

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:
\[6:2 \ne 7:3\]

Answer 8

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

Answer 9

so, what is the right option?

Answer 10

b?

Answer 11

sorry i got caught up

Answer 12

@Michele_Laino is b right?

Answer 13

correct!

Answer 14

thank you! :)