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Do triangles always have three lines of symmetry?
No, scalene triangles, which have sides of different lengths, have none. Isosceles triangles, with only two sides the same, only have one.
Is it true that No scalene triangles are similar?
Oh, no, that isn't true. We could have a scalene triangle with sides of, say, 2 cm, 3 cm, and 4 cm. Then we could have another scalene triangle with sides of 4 cm, 6 cm, and 8 cm. These two triangles would be similar because they have a ratio of 1:2, despite the fact that they are scalene. The term 'scalene' has nothing to do with similarity; it just means that a triangle has no equal sides.
Is that true that if two congruents triangles are always similar?
Yes.
Are two obtuse triangles sometimes always or never similar?
sometimes
Are two equilateral triangles sometimes always or never similar to each other?
Since triangles have three sides and must have interior angles equal to pi or 180o, the three interior angles in all equilateral triangles will be pi/3 or 60o.However, equilateral triangles must also have equal side lengths. Since equilateral triangles with interior angles of 60o will not necessarily have the same side lengths, two equilateral triangles will sometimes be similar to each other.
