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anonymous
 one year ago
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anonymous
 one year ago
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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Do you know the definition of an isosceles triangle?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1An 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
 one year ago
Best ResponseYou've already chosen the best response.1In an isosceles triangle, the angles opposite the congruent sides are congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439395982729:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1If an isosceles triangle is also equilateral, then all angles are also congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let'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.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1This means we are dealing with an isosceles triangle with only two congruent sides and only two congruent angles.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Here is a case of an isosceles triangle having 2 65deg angles. This is perfectly fine since 65 + 65 + 50 = 180. The top angle measures 50 degrees. dw:1439396229682:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we know that at least one isosceles triangle with a 65deg angle exists. The question we still have is whether there is another isosceles triangle with a 65deg angle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439396409264:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1What about the isosceles triangle above? It also has a 65degree angle, but it's the vertex angle, not the base angles.
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