yes just because it has different sizes it doesn't mean there is not such thing. yes.
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An acute triangle can be an isosceles triangle, but it doesn't have to be. An isosceles triangle can be an acute triangle, but it doesn't have to be.
no
An acute isosceles triangle has three acute angles (
Yes, but a triangle is acute only if all three of its angles are acute (< 90o).An isosceles triangle can be an acute triangle, but it doesn't have to be.An acute triangle can be an isosceles triangle, but it doesn't have to be.That depends on the sizes of its angle because an isosceles triangle has 2 equal sides and 2 equal angles which could be 70 degrees, 70 degrees and 40 degrees which are all acute angles that add up to 180 degrees.
Yes, that's possible. For instance a triangle with the angles 70°, 70° and 40° is both acute and isosceles.