Assertion: triangle | /r/HasProperty | equilateral
Facets:
Source sentences:
text: A triangle can be an equilateral
text: A triangle with all sides equal is called equilateral, a triangle with two sides equal is called isosceles, and a triangle with all sides a different length is called scalene.
text: For example, a triangle in which all three sides have equal lengths is called an equilateral triangle while a triangle in which two sides have equal lengths is called isosceles.
text: It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral.
text: both again holding if and only if the triangle is equilateral.
text: For some pairs of triangle centers, the fact that they coincide is enough to ensure that the triangle is equilateral.
text: A triangle is equilateral if any two of the circumcenter, incenter, centroid, or orthocenter coincide.  : p.37
text: A triangle is equilateral if and only if any three of the smaller triangles have either the same perimeter or the same inradius.  :
text: A triangle is equilateral if and only if the circumcenters of any three of the smaller triangles have the same distance from the centroid.
text: A triangle is equilateral if and only if, for every point P in the plane, with distances p, q, and r to the triangle's sides and distances x, y, and z to its vertices,: p.178,#235.4
text: As these triangles are equilateral, their altitudes can be rotated to be vertical.
text: A version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral.
text: The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest area of all those circumscribed around a given circle is equilateral.
text: The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest area of all those circumscribed around a given circle is equilateral.
text: There are numerous triangle inequalities that hold with equality if and only if the triangle is equilateral.
text: If a triangle is equilateral, what is the degree measure of each of its angles?
text: A triangle with all three equal sides is called equilateral.
text: A triangle that has all congruent angles and sides is called an equilateral triangle.