Question

Which statement is needed to prove that segment DE is parallel to segment BC and half its length?

Segment AD is 5 and segment AE is 4.

Segment AD is 4 and segment AE is 8.

Segment AD is 4 and segment AE is 5.

Segment AD is 5 and segment AE is 2.

Answer 1

@mathmale

Answer 2

IDK. :( I'm sorry..

Answer 3

I haven't done any formal proofs for many years, but do have some ideas for you that may be helpful. We do not have enough info YET to be able to say conclusively that Line DE is parallel to line BC. What additional info would we need to be able to do that?

Answer 4

the length?

Answer 5

While DE looks parallel to BC in the diagram, "looks" are not sufficient to say that the two lines actually are parallel.

I do see that there are 2 main triangles in this diagram: ADE and ABC, and that ADE and ABC share a common angle, angle A.

Would it help to state that triangles ADE and ABC are SIMILAR?

I have more ideas, but am now waiting to hear what YOU think.

Answer 6

EnchiladaMan: Length of what?

Answer 7

xD the length of the lines?

Answer 8

ChimichangaMan: length of which lines?

Answer 9

Actually, I'd urge you to consider the implications of declaring that triangles ADE and ABC are similar. What do you think those implications are?

Answer 10

there equilateral triangles?

Answer 11

Good start. But when I look closely, I see that all three sides of each triangle seem to be unique (that is, of different lengths).

Answer 12

Hey, FlauntaMan: If we accept the statement that the two triangles are similar ( a very important and helpful concept ), then we can conclude that angles ADE and ABC are EQUAL. Do you agree or disagree? Why?

Answer 13

i disagree? umm lol because there not the same lenghts

Answer 14

But we're comparing angles now, not lengths of sides.

Answer 15

Please go back and look at the diagram. Can you easily identify angle ABC? Angle ADE?
Do these angles appear to be equal or unequal?

Answer 16

ohh lol equal

Answer 17

If the 2 triangles are similar, then those 2 angles are indeed equal!

Answer 18

okay lol but im still stuck on the question

Answer 19

I don't know the name of the theorem, but there certainly is such a theorem:

If line AB intersects both of the lines DE and BC, and the angles thus created are equal (which they are, by similar triangles),

Answer 20

then lines BC and DE are parallel.

Have you seen and used such a theorem before?

Answer 21

i think its the first on because you would divide 10 by 2 and get 5 then you would do the same for 8

Answer 22

OK: Let's test your assumption that the first answer is the correct one:

Answer 23

I must agree with you. AD = 5 is half of AB, or 10/2;
AE = 4 is half of AC = 8/2.

Congrats!

The method I used, while correct, is more complicated than we need to prove that DE and BC are parallel.

Answer 24

thanks for all the help! :)

Answer 25

You're very welcome. De nada. Enjoy tonight's beef burrito.