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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

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  1. BIGDOG96
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    • one year ago
  2. TheMind
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    |dw:1347551396246:dw|

    • one year ago
  3. BIGDOG96
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    What are the blanks? If you don't mind me asking.

    • one year ago
  4. ganeshie8
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    4th row we need to fill

    • one year ago
  5. ganeshie8
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    so lets see whats happening in the next row - 5th one

    • one year ago
  6. BIGDOG96
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    4th and 6th

    • one year ago
  7. ganeshie8
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    yea in 5th row, we are using AA similarity. which means we need two congruent Angles ?

    • one year ago
  8. BIGDOG96
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    Okay

    • one year ago
  9. ganeshie8
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    did u understand 3rd row ?

    • one year ago
  10. BIGDOG96
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    Not really, I'm not good with Postulates.

    • one year ago
  11. ganeshie8
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    |dw:1347552555431:dw|

    • one year ago
  12. ganeshie8
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    look at the pix, DE is parallel to AC, its given

    • one year ago
  13. BIGDOG96
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    Yes, I understand that.

    • one year ago
  14. ganeshie8
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    now lets do some imagination

    • one year ago
  15. BIGDOG96
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    Alright

    • one year ago
  16. ganeshie8
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    think, you slide the side AC up and put it over DE

    • one year ago
  17. ganeshie8
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    |dw:1347552973501:dw|

    • one year ago
  18. BIGDOG96
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    Got it.

    • one year ago
  19. ganeshie8
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    then, since both lines are parallel, if you shrink AC, A overlaps wid D and C overlaps with E

    • one year ago
  20. ganeshie8
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    <A = <D

    • one year ago
  21. ganeshie8
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    <C = <E

    • one year ago
  22. ganeshie8
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    right ?

    • one year ago
  23. BIGDOG96
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    Yes

    • one year ago
  24. ganeshie8
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    since two sets of corresponding angles are equal, both triangles, small and big ones, are similar

    • one year ago
  25. BIGDOG96
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    Yes

    • one year ago
  26. ganeshie8
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    |dw:1347553320251:dw|

    • one year ago
  27. ganeshie8
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    so 4th statement can we have like this : < BED \(\cong\) <BCA by "Corresponding Angles Postulate" ?

    • one year ago
  28. BIGDOG96
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    Agreed

    • one year ago
  29. ganeshie8
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    |dw:1347553430140:dw|

    • one year ago
  30. ganeshie8
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    good lets think of last row

    • one year ago
  31. BIGDOG96
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    Okay

    • one year ago
  32. ganeshie8
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    last row must contain the thing asked for proving

    • one year ago
  33. BIGDOG96
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    Prove: BD over BA equals BE over BC

    • one year ago
  34. ganeshie8
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    yea so lets put the last statement as \( \frac{BD}{BA} = \frac{BE}{BC} \)

    • one year ago
  35. ganeshie8
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    can you think of what will be the Reason/justification ?

    • one year ago
  36. BIGDOG96
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    Um to be honest I have no idea...........Like I said I'm horrible at justifications.

    • one year ago
  37. BIGDOG96
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    So the answer is BDBA=BEBC "Corresponding sides of similar triangles are proportional"?

    • one year ago
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