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anonymous

  • one year ago

Prove that the base angles of an isosceles triangle are congruent. Be sure to create and name the appropriate geometric figures. I really need to pass this class! So any help would be amazing!

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  1. TheSmartOne
    • one year ago
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    @dan815 @Michele_Laino @triciaal QH question

  2. anonymous
    • one year ago
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    http://www.regentsprep.org/regents/math/geometry/gp6/Lisosceles.htm

  3. Michele_Laino
    • one year ago
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    we have to consider the height of your triangle with respect to its base, namely: |dw:1435251966017:dw|

  4. anonymous
    • one year ago
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    Ok but If I have to show this in text, because I cannot post pictures. So if i had to type out an explanation how would I do that?

  5. dan815
    • one year ago
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    well u gotta prove the height is connected to the mid point of the base too :P

  6. Michele_Laino
    • one year ago
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    now, there exists a theorem which states that for an isosceles triangle the heigh with respect to its base is also a median of its base and bisects the angle at vertex C. In other words the angles ACH and BCH are congruent, and AH is congruent to BH |dw:1435252103138:dw|

  7. dan815
    • one year ago
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    |dw:1435252124559:dw|

  8. TheSmartOne
    • one year ago
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    You could even use a 4-45-90 triangle. |dw:1435252159759:dw|

  9. TheSmartOne
    • one year ago
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    45-45-90 **

  10. Michele_Laino
    • one year ago
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    now, using the criterion SAS we can states that the two triangles ACH and BCH are congruents each other, in particular the two angles CAH and CBH are congruent each other

  11. anonymous
    • one year ago
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    I am still so confused...

  12. anonymous
    • one year ago
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    @Michele_Laino I dont understand any of this...

  13. dan815
    • one year ago
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    okay here ill show u how i d do it i think this is a simple way

  14. dan815
    • one year ago
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    |dw:1435252537882:dw|

  15. Michele_Laino
    • one year ago
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    we have to consider the height CH of the triangle with respect to the base: |dw:1435252513714:dw| by hypothesis we have AC=BC, right?

  16. dan815
    • one year ago
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    |dw:1435252556250:dw|

  17. Michele_Laino
    • one year ago
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    step #2 exixts a theorem which states that the height CH is also the bisector of the angle ACB: |dw:1435252664811:dw| so the angles ACH and BCH are congruent each other

  18. TheSmartOne
    • one year ago
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    yo dan, you're going to confuse her with the alpha and beta :p

  19. TheSmartOne
    • one year ago
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    \(\sf\alpha\) and \(\sf\beta\) are just variables used for angles, repectively called alpha and beta.

  20. Michele_Laino
    • one year ago
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    step #3 the two triangle ACH and BCH are congruent by the criterion SAS being the side CH in common

  21. Michele_Laino
    • one year ago
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    triangles*

  22. anonymous
    • one year ago
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    Yeah.... I dont get that at all...alpha and beta?

  23. TheSmartOne
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @camzzz12 Ok but If I have to show this in text, because I cannot post pictures. So if i had to type out an explanation how would I do that? \(\color{blue}{\text{End of Quote}}\) Your question states: "Be sure to create and name the appropriate geometric figures."

  24. anonymous
    • one year ago
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    I know, but I dont have a place to put a picture, It only allows me to submit text...

  25. TheSmartOne
    • one year ago
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    Maybe an attach file button?

  26. anonymous
    • one year ago
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    There is none, I looked for it before but I dont see one. All that there is, is a text box and the question

  27. Michele_Laino
    • one year ago
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    step #4 in particular angles CAH and CBH are congruent each other |dw:1435252914983:dw|

  28. TheSmartOne
    • one year ago
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    Ok, let me try to explain to you what Dan said as the Alpha and Beta confused you.

  29. anonymous
    • one year ago
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    Please do...

  30. dan815
    • one year ago
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    use my proof its nice :) no theorems needed

  31. TheSmartOne
    • one year ago
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    |dw:1435252952954:dw|

  32. TheSmartOne
    • one year ago
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    So we have a triangle. Do you understand up until here?

  33. anonymous
    • one year ago
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    Yes I understand that we have a triangle

  34. TheSmartOne
    • one year ago
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    Ok, have you learned what reflection is in math?

  35. dan815
    • one year ago
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    ok well thats not true I used the SSS theorem xD

  36. anonymous
    • one year ago
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    Yes

  37. TheSmartOne
    • one year ago
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    so lets reflect this triangle that we have along our imaginary x-axis |dw:1435253100351:dw|

  38. TheSmartOne
    • one year ago
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    still with me?

  39. anonymous
    • one year ago
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    yes

  40. TheSmartOne
    • one year ago
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    So now lets put these two triangles together and combine them:

  41. TheSmartOne
    • one year ago
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    |dw:1435253288145:dw|

  42. anonymous
    • one year ago
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    ok so how does this help prove that the base angles are congruent?

  43. TheSmartOne
    • one year ago
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    so lets put values for our sides

  44. TheSmartOne
    • one year ago
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    |dw:1435253562066:dw|

  45. TheSmartOne
    • one year ago
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    so that means: |dw:1435253593981:dw|

  46. TheSmartOne
    • one year ago
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    you can see that if you look at one triangle at a time that the angle 60 has a side length of √3 if you look at the whole triangle as a whole, you can see that the two angle 60 has a side length of 2

  47. anonymous
    • one year ago
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    I dont understand that....

  48. TheSmartOne
    • one year ago
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    |dw:1435253906377:dw|

  49. TheSmartOne
    • one year ago
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    |dw:1435253954503:dw|

  50. TheSmartOne
    • one year ago
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    This website also has another way to explain it: http://www.basic-mathematics.com/base-angles-theorem.html

  51. anonymous
    • one year ago
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    Omg that other website helps me so much! Thank you so much

  52. TheSmartOne
    • one year ago
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    haha, no problem :)

  53. anonymous
    • one year ago
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    I guess im going to close this question now, so again, thank you so much for all of your help!!!!! :) <3

  54. TheSmartOne
    • one year ago
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    Anytime :)

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