Obtuse trianglesĪ triangle is obtuse if one of its angles is greater than 90 degrees.Īn obtuse isosceles triangle has a wide base, which means that the top angle (the angle where the legs meet) is larger than 90 degrees. Acute trianglesĪ triangle is acute if all three of its angles are less than 90 degrees.Īll the triangles shown above are acute. Scalene trianglesĪ scalene triangle has three unequal sides.Īll three angles in a scalene triangle are also unequal. We sometimes call the two equal sides the legs of the triangle, and the other side the base.Įach leg makes an equal angle with the base. The third side is not equal to the other two (it can be longer or shorter). Isosceles trianglesĪn isosceles triangle has two sides that are equal in length. All equilateral triangles are the same shape, but can be different sizes (we say they are similar). Since the three angles of any triangle always add up to 180 degrees, it follows that each angle in an equilateral triangle must be equal to 60 degrees.Īnd equilateral triangle is a regular polygon. The angle arcs in the corners indicate that the angles are all equal. The tick marks on the three sides indicate that the sides are the same length. Equilateral trianglesĪn equilateral triangle is a triangle where all three sides are the same length, and all three angles are equal: The angles inside any triangle add up to 180 degrees. Obtuse, where one angle is greater than 90 degrees.Right-angled, where one angle is exactly 90 degrees.Acute, where all three angles are less than 90 degrees.Isosceles and scalene triangles can be divided into three types: Scalene triangles, where none of the sides are equal and none of the angles are equal.Isosceles triangles, that have two equal sides and two equal angles.Equilateral triangles, that have three equal sides and three equal angles.Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.A triangle is a shape with three straight sides. When possible we just find it easier to think, and problem solve, in mathematics, with inclusive definitions. It also has two equal angles (and more)!Īcute is a somewhat different property but clearly all angles of an equilateral triangle are less than 90 degrees. So - back to triangles: An Equilateral Triangle is still Isosceles. You don't say that the construction 'failed'! It just was inclusive of all the objects you found, and included the rectangle and square as possible examples. If you use the key positive properties to define what a parallelogram is, and then start moving things around, one of the images that appears is a rectangle, maybe even a square. the formula for the area of a rectangle still works for a square,Ī second way to 'see' this is to consider constructions in a dynamic geometry program (like Geometer's SketchPad).

diagonals bisect in a parallelogram) still apply to the special cases (e.g. One way to see that this is useful, is to realize that any special properties from the larger class:Į.g. So a square IS still a rectangle (still has four right angles!). In mathematics, the usual way to work with classifications / definitions is as 'inclusive' properties.Īs long an object retains the key property, it remains in the category, even if some extra properties come up. If all sides of a triangle are the same length and all angles are 60 degrees, can the triangle be called both an acute triangle and an equilateral triangle? Can the triangle be called both an acute triangle and an equilateral triangle?- Math Central

Triangle isosceles acute