Isosceles triangle is acute, right or obtuse depends only on the angle at its apex. In Euclidean geometry, the base angles cannot be obtuse (greater than 90°) or right (equal to 90°) because their measures would sum to at least 180°, the total of all angles in any Euclidean triangle. Since a triangle is obtuse or right if and only if one of its angles is obtuse or right, respectively, an isosceles triangle is obtuse, right or acute if and only if its apex angle is respectively obtuse, right or acute. In Edwin Abbott's book "Flatland", this classification of shapes was used
Heptagonal triangle Heptagonal triangle A heptagonal triangle is an obtuse scalene triangle whose vertices coincide with the first, second, and fourth vertices of a regular heptagon (from an arbitrary starting vertex). Thus its sides coincide with one side and the adjacent shorter and longer diagonals of the regular heptagon. All heptagonal triangles are similar (have the same shape), and so they are collectively known as "the" heptagonal triangle. Its angles have measures formula_1 and formula_2 and it is the only triangle with angles in the ratios 1:2:4. The heptagonal triangle has various remarkable properties. The heptagonal triangle's nine-point center is also its