equilateral triangle
a triangle with 3 congruent sides
An equilateral triangle is a triangle in which all three sides are of equal length. Additionally, all three angles within an equilateral triangle are equal to 60 degrees. An equilateral triangle is a unique type of isosceles triangle, which has two sides of equal length, but does not necessarily have equal angles.
Due to the symmetry of its sides and angles, an equilateral triangle has several unique properties. Here are some of them:
– The three medians and three altitudes of an equilateral triangle are all equal, and they all intersect at the same point, known as the centroid or center of mass.
– The perimeter of an equilateral triangle can be computed by multiplying the length of one side by 3. That is, P = 3s, where P is the perimeter and s is the length of each side.
– The area of an equilateral triangle can be calculated as A = (s^2 * sqrt(3))/4, where A is the area and s is the length of each side.
– Equilateral triangles can be used to create tessellations, where they are arranged in a repeating pattern to cover a plane without any gaps or overlaps.
– Equilateral triangles have rotational symmetry of order three, which means that they can be rotated by multiples of 60 degrees to look the same again.
In summary, an equilateral triangle is a special type of triangle with all sides and angles equal, and it has several unique properties that make it useful in various mathematical and geometric applications.
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