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anonymous

  • one year ago

HELP!! MEDAL + FAN Use the figure below to answer the question that follows: What must be given to prove that ΔBJI ~ ΔCJG? A. segment BH is congruent to segment CH and segment BG is congruent to segment CI B. ∠BIJ ≅ ∠CGJ and ∠JBI ≅ ∠JIB C. segment BI is congruent to segment CG and D. segment JI is congruent to segment JG ∠BIJ ≅ ∠CGJ and ∠BJI ≅ ∠CJG

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @peachpi @Hero @welshfella @ganeshie8 @theopenstudyowl

  3. mathstudent55
    • one year ago
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    Which methods of proving triangles similar do you know?

  4. anonymous
    • one year ago
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    SAS, SA, SSS

  5. anonymous
    • one year ago
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    angle side*

  6. mathstudent55
    • one year ago
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    I know: AA SAS Similarity SSS Similarity

  7. anonymous
    • one year ago
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    aa yes sorry i forgot that one.

  8. mathstudent55
    • one year ago
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    In your given problem, do the triangles have any pair of sides or angles that is congruent?

  9. anonymous
    • one year ago
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    yes

  10. mathstudent55
    • one year ago
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    |dw:1441305297304:dw|

  11. mathstudent55
    • one year ago
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    I drew the figure twice above because the triangles we are trying to prove similar overlap, so I think it's easier to separate the figures.

  12. mathstudent55
    • one year ago
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    |dw:1441305484271:dw|

  13. mathstudent55
    • one year ago
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    This new figure shows the triangles we want to prove similar. Which pair of angles or sides do they have in common that we know are congruent?

  14. anonymous
    • one year ago
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    BF and EC?

  15. mathstudent55
    • one year ago
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    No. We are not told anything bout BF and EC, and also, BF and EC are not sides of our two triangles.

  16. mathstudent55
    • one year ago
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    |dw:1441305708106:dw|

  17. anonymous
    • one year ago
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    BIJ

  18. mathstudent55
    • one year ago
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    Look at the figure above. Angle J is in common to both triangles, so we already have a pair of congruent corresponding angles.

  19. mathstudent55
    • one year ago
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    <BJI and <CJG are congruent because they are really the same angle.

  20. mathstudent55
    • one year ago
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    Since we already have a pair of congruent angles, we will probably use AA or SAS Similarity, and not SSS Similarity.

  21. mathstudent55
    • one year ago
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    To use AA, we need one more pair of corresponding angles that are congruent. Let's look at the choices.

  22. anonymous
    • one year ago
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    Wouldnt it be CJG? like it says there

  23. mathstudent55
    • one year ago
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    In choice B, the congruent angles are not corresponding, so they don't help.

  24. mathstudent55
    • one year ago
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    In choice A, the segments are not sides of our triangle, so choice A does not help.

  25. anonymous
    • one year ago
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    So its between choice C and D.

  26. mathstudent55
    • one year ago
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    In choice C, we have only one pair of corresponding sides congruent. That is not enough for SAS Similarity.

  27. mathstudent55
    • one year ago
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    Let's try D.

  28. anonymous
    • one year ago
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    D makes more sense to me

  29. mathstudent55
    • one year ago
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    Yes, choice D shows a pair of congruent sides and two pairs of congruent angles. Using the two pairs of congruent angles of choice D, we can prove the triangles similar by AA.

  30. anonymous
    • one year ago
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    Thank you so much for helping!

  31. mathstudent55
    • one year ago
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    You're welcome.

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