anonymous
  • anonymous
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Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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anonymous
  • anonymous
You're good
anonymous
  • anonymous
am i right

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mathstudent55
  • mathstudent55
Do you know the definition of an isosceles triangle?
anonymous
  • anonymous
yes
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
In an isosceles triangle, the angles opposite the congruent sides are congruent.
mathstudent55
  • mathstudent55
|dw:1439395982729:dw|
mathstudent55
  • mathstudent55
If an isosceles triangle is also equilateral, then all angles are also congruent.
mathstudent55
  • mathstudent55
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.
anonymous
  • anonymous
okay
mathstudent55
  • mathstudent55
This means we are dealing with an isosceles triangle with only two congruent sides and only two congruent angles.
mathstudent55
  • mathstudent55
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|
anonymous
  • anonymous
okay
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
|dw:1439396409264:dw|
anonymous
  • anonymous
so it is A
mathstudent55
  • mathstudent55
What about the isosceles triangle above? It also has a 65-degree angle, but it's the vertex angle, not the base angles.
mathstudent55
  • mathstudent55
Correct.
anonymous
  • anonymous
thanks
mathstudent55
  • mathstudent55
You're welcome.

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