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Yes, it is true that an isosceles triangle can be acute or obtuse. As long as a triangle has two equal angles and two equal sides, it is isosceles. That situation can occur in both acute (all angles less than 900) and obtuse (one angle more than 900) triangles.
Examples are a triangle with the angles being 75-75-30 degrees (acute) and one having angles of 120-30-30 (obtuse). Of course the sides of the angles that are equal would also be equal, so both examples are of isosceles triangles.
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Is it true that isosceles triangles may be obtuse or acute but never right?
No, it is not true.
Is it true that an obtuse triangle has two obtuse angles and one acute angle?
No
Can an Isosceles triangles may be obtuse or acute but never right?
Not true. A triangle with angles of 90, 45 and 45 is a right angled isosceles triangle. If you take a square piece of paper and fold it in half - from corner to corner - you will get this shape.
Does obtuse triangle have any angles congruent?
An obtuse triangle must have two acute angles and these can be congruent.
Is it true that a obtuse triangle has a greater area than any acute triangle?
Not at all.
