Isosceles triangles (that can be acute, obtuse, or right-angled).Equilateral triangles (that are always acute).The sum of the two angles at the base is 90 degrees.Īn equilateral triangle can't be right-angled, because all the angles of an equilateral triangle are 60 degrees. They can be different sizes (they are similar).Ī right-angled scalene triangle is similar, but the legs are different sizes:
This means that all right-angled isosceles triangles are the same shape. Since we know that the other angle is 90 degrees, this means that the two angles at the base must both be equal to 45 degrees (because 90 + 45 + 45 is 180). Here is a right-angled isosceles triangle:Īs before the two legs of an isosceles triangle are the same length and the two angles at the base are equal. Right-angled trianglesĪ right-angled triangle has one angle of exactly 90 degrees. One of the angles has a measure of 90° as it is a right triangle. 57° + 90° + x 180° The sum of the three angles of a triangle is 180 °. It is impossible for a triangle to have more than one angle that is greater than 90 degrees because the sum of all three angles is 180 degrees.Īn equilateral triangle can't be obtuse, because all the angles of an equilateral triangle are 60 degrees. One of the angles in a right triangle measures 57º. In this case, all the sides have different lengths and all the angles are different, but the shape has one angle that is greater than 90 degrees. The two legs are the same length, and the two angles at the base are equal. 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.Note that from the definitions, an equilateral triangle is also an isosceles triangle.A triangle is a shape with three straight sides.
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