## BIGDOG96 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. one year ago one year ago

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"?