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BIGDOG96

Given: In ∆ABC below,BD over BA equals BE over BC . Prove: segment DE is parallel to segment AC The flow chart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side. Which statement and reason can be used to fill in the numbered blank spaces? Answers 1. ∡BDE ≅ ∡BAC 2. Corresponding Parts of Similar Triangles 1. ∡BDE ≅ ∡BCA 2. Alternate Exterior Theorem 1. ∡BDE ≅ ∡BAC 2. Corresponding Angles Postulate 1. ∡BDE ≅ ∡BCA 2. Corresponding Parts of Similar

  • one year ago
  • one year ago

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  1. BIGDOG96
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    • one year ago
  2. BIGDOG96
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    I think it's A.

    • one year ago
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  3. ganeshie8
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    see the justification for statement after blank

    • one year ago
  4. BIGDOG96
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    Yes

    • one year ago
  5. ganeshie8
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    they have used "Converse of Corresponding Angles Postulate" what does that mean ?

    • one year ago
  6. BIGDOG96
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    Opposite?

    • one year ago
  7. ganeshie8
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    Converse of Corresponding Angles Postulate says, if corresponding angles are equal, then the lines are parallel

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  8. BIGDOG96
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    Oh

    • one year ago
  9. ganeshie8
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    so we need to prove two corresponding angles are congruent

    • one year ago
  10. BIGDOG96
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    Ah I see

    • one year ago
  11. ganeshie8
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    have a look at the triangle now

    • one year ago
  12. ganeshie8
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    <BDE and <BAC are corresponding anlges, right ?

    • one year ago
  13. BIGDOG96
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    Yes

    • one year ago
  14. ganeshie8
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    they are corresponding angles, cuz \(\triangle BDE\) and \(\triangle BAC\) are similar,

    • one year ago
  15. BIGDOG96
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    Yes, that makes the 3rde choice make sense.

    • one year ago
  16. ganeshie8
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    now can we say they are congruent, cuz corresponding angles of similar triangles are congruent ?

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  17. BIGDOG96
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    Yes

    • one year ago
  18. ganeshie8
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    so which one is it ?

    • one year ago
  19. BIGDOG96
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    3

    • one year ago
  20. ganeshie8
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    it cannot be 3rd cuz, we dont know lines are parallel yet

    • one year ago
  21. ganeshie8
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    notice the justification for 3rd one

    • one year ago
  22. BIGDOG96
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    Then A?

    • one year ago
  23. ganeshie8
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    yup ! you need to be careful about justification also

    • one year ago
  24. BIGDOG96
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    Right

    • one year ago
  25. ganeshie8
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    before the blank, we proved triangles are similar, in the blank, we use it

    • one year ago
  26. BIGDOG96
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    Oh, got cha

    • one year ago
  27. ganeshie8
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    :)

    • one year ago
  28. BIGDOG96
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    Two more questions.

    • one year ago
  29. ganeshie8
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    sure

    • one year ago
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