Can an equilateral triangle have an obtuse angle?

I'm thinking not, because all sides must be equal, but
does that also imply that all angles are equal?



Hi Chris. You are right - an equilateral triangle cannot have an obtuse angle. In fact, the angles are all "fixed" - they are each 60 degrees.

Try this: take three equal length pencils and form a triangle. Now take three more pencils and try to form a triangle that has angles different from the first. Don't try too hard of course: it isn't actually possible.

In fact, in any triangle when you have even two sides the same length, that means their opposite angles are also the same size. That's an isosceles triangle. An equilateral triangle has all three sides the same, therefore all three angles are the same. When you add up the angles of any triangle, you get 180 degrees, so 180 divided by 3 is 60 - the size of every angle of any equilateral triangle.

Stephen La Rocque>