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anonymous

  • one year ago

answer check

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    You're good

  3. anonymous
    • one year ago
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    am i right

  4. mathstudent55
    • one year ago
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    Do you know the definition of an isosceles triangle?

  5. anonymous
    • one year ago
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    yes

  6. mathstudent55
    • one year ago
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    An isosceles triangle is a triangle that has at least two congruent sides. This means an isosceles triangle can have 2 congruent sides or 3 congruent sides.

  7. mathstudent55
    • one year ago
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    In an isosceles triangle, the angles opposite the congruent sides are congruent.

  8. mathstudent55
    • one year ago
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    |dw:1439395982729:dw|

  9. mathstudent55
    • one year ago
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    If an isosceles triangle is also equilateral, then all angles are also congruent.

  10. mathstudent55
    • one year ago
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    Let's look at an equilateral triangle first. Since you want one angle to measure 65 deg, then all angles would have to measure 65 degrees. This is a problem, because 65 + 65 + 65 > 180 and the sum of the measure of the angles of a triangle is 180, not more than 180. We now know we are not dealing with an equilateral triangle.

  11. anonymous
    • one year ago
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    okay

  12. mathstudent55
    • one year ago
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    This means we are dealing with an isosceles triangle with only two congruent sides and only two congruent angles.

  13. mathstudent55
    • one year ago
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    Here is a case of an isosceles triangle having 2 65-deg angles. This is perfectly fine since 65 + 65 + 50 = 180. The top angle measures 50 degrees. |dw:1439396229682:dw|

  14. anonymous
    • one year ago
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    okay

  15. mathstudent55
    • one year ago
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    Now we know that at least one isosceles triangle with a 65-deg angle exists. The question we still have is whether there is another isosceles triangle with a 65-deg angle.

  16. mathstudent55
    • one year ago
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    |dw:1439396409264:dw|

  17. anonymous
    • one year ago
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    so it is A

  18. mathstudent55
    • one year ago
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    What about the isosceles triangle above? It also has a 65-degree angle, but it's the vertex angle, not the base angles.

  19. mathstudent55
    • one year ago
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    Correct.

  20. anonymous
    • one year ago
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    thanks

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

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