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BIGDOG96

  • 2 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.

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  1. BIGDOG96
    • 2 years ago
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  2. TheMind
    • 2 years ago
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    |dw:1347551396246:dw|

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

  4. ganeshie8
    • 2 years ago
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    4th row we need to fill

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

  6. BIGDOG96
    • 2 years ago
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    4th and 6th

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

  8. BIGDOG96
    • 2 years ago
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    Okay

  9. ganeshie8
    • 2 years ago
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    did u understand 3rd row ?

  10. BIGDOG96
    • 2 years ago
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    Not really, I'm not good with Postulates.

  11. ganeshie8
    • 2 years ago
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    |dw:1347552555431:dw|

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

  13. BIGDOG96
    • 2 years ago
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    Yes, I understand that.

  14. ganeshie8
    • 2 years ago
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    now lets do some imagination

  15. BIGDOG96
    • 2 years ago
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    Alright

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

  17. ganeshie8
    • 2 years ago
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    |dw:1347552973501:dw|

  18. BIGDOG96
    • 2 years ago
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    Got it.

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

  20. ganeshie8
    • 2 years ago
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    <A = <D

  21. ganeshie8
    • 2 years ago
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    <C = <E

  22. ganeshie8
    • 2 years ago
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    right ?

  23. BIGDOG96
    • 2 years ago
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    Yes

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

  25. BIGDOG96
    • 2 years ago
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    Yes

  26. ganeshie8
    • 2 years ago
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    |dw:1347553320251:dw|

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

  28. BIGDOG96
    • 2 years ago
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    Agreed

  29. ganeshie8
    • 2 years ago
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    |dw:1347553430140:dw|

  30. ganeshie8
    • 2 years ago
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    good lets think of last row

  31. BIGDOG96
    • 2 years ago
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    Okay

  32. ganeshie8
    • 2 years ago
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    last row must contain the thing asked for proving

  33. BIGDOG96
    • 2 years ago
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    Prove: BD over BA equals BE over BC

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

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

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

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

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