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Can an isosceles triangle have 3 equal angles?

  1. May 9, 2015 #1
    Okay, I know I must sound like a complete idiot here, but please bear with me.

    I've come across a scenario in which I have triangle ECF. Angle ECF = 60 degrees, Angles CEF and CFE are unknown, lengths EC and FC are unknown and equal and length EF is r√3 and not equal to lengths EC and FC

    I know it has to be an isosceles triangle, but because angle ECF = 60 the remaining angles must both also be equal to 60 degrees.

    I'm not sure if this is possible or not. Also, sorry if this is a very basic question but I have honestly never encountered this scenario before. Any help is much appreciated.
  2. jcsd
  3. May 9, 2015 #2


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    Homework Helper

    This is an impossible object.

    However, isosceles triangles can have 3 equal angles, and it becomes a special type of isosceles triangle - the equilateral triangle. This is equivalent to a square being a special type of rectangle, which itself is a special type of parallelogram, which is a special quadrilateral.
  4. May 9, 2015 #3


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    2017 Award

    Staff: Mentor

    Such a triangle is possible on a sphere and some other objects, but not on a plane.
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