## BIGDOG96 3 years ago 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. Complete the proof by entering the correct statements and reasons.

1. BIGDOG96

2. TheMind

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3. BIGDOG96

What are the blanks? If you don't mind me asking.

4. ganeshie8

4th row we need to fill

5. ganeshie8

so lets see whats happening in the next row - 5th one

6. BIGDOG96

4th and 6th

7. ganeshie8

yea in 5th row, we are using AA similarity. which means we need two congruent Angles ?

8. BIGDOG96

Okay

9. ganeshie8

did u understand 3rd row ?

10. BIGDOG96

Not really, I'm not good with Postulates.

11. ganeshie8

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12. ganeshie8

look at the pix, DE is parallel to AC, its given

13. BIGDOG96

Yes, I understand that.

14. ganeshie8

now lets do some imagination

15. BIGDOG96

Alright

16. ganeshie8

think, you slide the side AC up and put it over DE

17. ganeshie8

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18. BIGDOG96

Got it.

19. ganeshie8

then, since both lines are parallel, if you shrink AC, A overlaps wid D and C overlaps with E

20. ganeshie8

<A = <D

21. ganeshie8

<C = <E

22. ganeshie8

right ?

23. BIGDOG96

Yes

24. ganeshie8

since two sets of corresponding angles are equal, both triangles, small and big ones, are similar

25. BIGDOG96

Yes

26. ganeshie8

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27. ganeshie8

so 4th statement can we have like this : < BED $$\cong$$ <BCA by "Corresponding Angles Postulate" ?

28. BIGDOG96

Agreed

29. ganeshie8

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30. ganeshie8

good lets think of last row

31. BIGDOG96

Okay

32. ganeshie8

last row must contain the thing asked for proving

33. BIGDOG96

Prove: BD over BA equals BE over BC

34. ganeshie8

yea so lets put the last statement as $$\frac{BD}{BA} = \frac{BE}{BC}$$

35. ganeshie8

can you think of what will be the Reason/justification ?

36. BIGDOG96

Um to be honest I have no idea...........Like I said I'm horrible at justifications.

37. BIGDOG96

So the answer is BDBA=BEBC "Corresponding sides of similar triangles are proportional"?