Question

Given: In ∆ABC, segment DE is parallel to segment AC .
Prove: BD over BA equals BE over BC
The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.

Statement

Reason
1. segment DE is parallel to segment AC

1. Given
2. Line segment BA is a transversal that intersects two parallel lines

2. Conclusion from Statement 1
3.

3.
4. ∡BDE ≅ ∡BAC

4. Reflexive Property of Equality
5. ∆ABC ~ ∆DBE

5. Angle-Angle (AA) Similarity Postulate
6.

6.


Complete the proof by entering the correct statements and reasons.

Answer 1

so this isn't multiple choice and it's more like type in the answer?

Answer 2

yea ..can u help??

Answer 3

yeah just need to think of the right wording, one sec

Answer 4

omg ur amazing thank you! lol ill wait take ur time:)

Answer 5

ugh, had a glitch, one sec while I retype, so sorry about that

Answer 6

basically in step 4, they're using the symmetric property and not the reflexive property...not sure why they made this mistake


So to get to step 4, we need to get ∡BAC ≅ ∡BDE for step 3 (this is just the flipped version of step 4)


So the answer for the first part of step 3 is ∡BAC ≅ ∡BDE


The justification for this step is that a transversal line creates corresponding congruent angles

--------------------------------

In step 5, we prove that the triangles are similar

So in step 6, we can say that the corresponding sides are proportional

Therefore, the answer for the first part in step 6 is

BD over BA equals BE over BC

and the justification for this step is

Side-Side-Side Similarity Theorem


again sry about that

Answer 7

haha no need for sorry hun!

Answer 8

hopefully all that makes sense and that you're able to input it the way they want it

Answer 9

its perfect thank you so much ..ur awesome:)

Answer 10

you're very welcome

Answer 11

<3

Answer 12

aww I'm touched lol

Answer 13

...or that could be ice cream...either way, sweet

Answer 14

hahaha both would be good! lol ..i want some ice cream now! lol hmmm

Answer 15

yes ice cream is always good no matter what time it is

Answer 16

haha ikr! ...i think i have some chocolate in the freezer! lol

Answer 17

lol then it's time to dive in, that sounds really delicious

Answer 18

hahaha come on over! lol

Answer 19

lol it's time to have an ice cream party

Answer 20

makes me wish I had some ice cream, lol I'm making myself hungry

Answer 21

hahaha ice cream party sounds fun! lol ...haha ikr! im to lazy to get up and go get some tho! lmao

Answer 22

lol so basically I have a better chance of getting at it than you do?

Answer 23

hahahahaha yes! i cant tell u how comfortable i am in my bed right now! lol

Answer 24

that makes sense, once I'm comfy in bed, I can't get out too

Answer 25

haha yea ...ice cream isnt that important! lol

Answer 26

lol I can see it folding its arms in the background saying "fine, I see how it is"

Answer 27

haha sorry....i would get up and get u some ice cream if u were here! lol

Answer 28

lol no i can manage on my own, so it's all good

Answer 29

haha ok ..good i didnt wanna get up anyways! lol

Answer 30

lol i knew that

Answer 31

haha u must be psychic or something! lmao:P

Answer 32

lol i wish

Answer 33

so where u from?

Answer 34

I'm born and raised in CA, still living here as well

Answer 35

cool i was born in Portugal and now i live in Florida! lol

Answer 36

very cool, I've been as close to florida since I passed through georgia, but have never been even close to portugal lol

Answer 37

haha yea i love it here we have nice beaches! ...yea alot of people havent my dad was in the military so thats why i was born there !

Answer 38

ah so you've basically seen most of the world then?

Answer 39

yes i have ive been alot of places!

Answer 40

my understanding (probably flawed though?) is that military families move a lot all over the world.

Answer 41

yes most of the time but not always! ..but my dads out of the military now so we r here for good! lol

Answer 42

oh very cool, seeing the world is great (don't get me wrong), but settling in a nice home is much much better.

Answer 43

yes i agree! but i dont remember alot of the traveling bc i was very little!

Answer 44

Ah that's a pity, but then again, you probably didn't have to deal with the hassles of changing schools and such. So that's good.

Answer 45

yea ur right! ..hey i have to go to bed its 1pm her! and im tired! but if ur on tomorrow message me:) ..it was nice to meet u my name is anna btw

Answer 46

Nice to meet you Anna, you obviously already know (from my username), but I might as well make it formal lol: I'm Jim. Yeah I'm not thinking of the time difference, lol it's really late over there.

Answer 47

Feel free to message me if you need any more help. You can also email me if you want if I'm not on and I might get to it much quicker.

Answer 48

ok jim well ill message u and then u can give me ur email:)

Answer 49

alright sounds good

Answer 50

@Coolsector

Answer 51

For those who see this and was as confused as I was it is
3. ∠ BDE ≅ ∠ BAC; Corresponding Angles Postulate
5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate