All isosceles triangles must have two congruent sides otherwise it is not isosceles. Whether it is acute angled, right angled or obtuse angled is irrelevant.
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acute angled triangle,right angled triangle,obtuse angled triangle,isosceles triangle,equilateral triangle, scalene triangle
An obtuse triangle or a right angle triangle. An equilateral is definitely an isoceles triangle * * * * * Not true. An obtuse or right angled triangles can be isosceles. It depends on the sizes of the two smaller angles. An isosceles triangle has two equal angles so a triangle with angles of size [A, (180-A)/2, (180-A)/2] degrees where 90 < A < 180 degrees would be an obtuse angled isosceles triangle. A triangle with angles of size (90, 45, 45) degrees is a right angled isosceles triangle.
Any of the above: you can have a right-angled isosceles (not isoscles!) triangle, or an obtuse-angled one or an acute angled-one.
The angle sum of any triangle is 180 degrees. It does not matter whether it is equilateral, isosceles or scalene, nor whether it is acute angled, right angled or obtuse angled (or any permitted combination).
Any kind of triangle can have rational or irrational sides: acute angled, right angled or obtuse angled; equilateral, isosceles or scalene.