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The equilateral triangle is also the only triangle that can have both rational side lengths and angles (when measured in degrees). When inscribed in a unit square, the maximal possible area of an equilateral triangle is \(2\sqrt{3}-3\), occurring when the triangle is oriented at a \(15^{\circ}\) angle and has sides of length \(\sqrt{6}-\sqrt{2}:\)
When comparing the lengths of a triangle's sides, all three sides may be equal, two sides may be equal, or all three sides may be different lengths. This observation forms the basis of a classification system. In an equilateral triangle, all sides are equal in length. ("Equilateral" is derived from two words: "equi" meaning "equal," and "lateral" ...
In other words, the equilateral triangle is in company with the circle and the sphere whose full structures are known only by knowing the radius. Equilateral Triangle Formula. Formulas for the area, altitude, perimeter, and semi-perimeter of an equilateral triangle are as given: Where, a is the side of an equilateral triangle. h is the altitude ...
A triangle with three equal sides is called as? Answer: Equilateral triangle. Question 3: What are the 7 types of triangles? Answer: The seven types of triangles that exist in the math are equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene. Question 4: What are the properties of a ...
An equilateral triangle is a triangle whose all three sides are having the same length. This is the only regular polygon with three sides. It appears in a variety of contexts, in both basic geometries as well as in many advanced topics such as complex number geometry and geometric inequalities.
This is an Equilateral Triangle. In equilateral triangles all the sides are equal. So we can say that they have identical sides and identical angles. No matter what is the length of the sides, angles in equilateral triangles have a measure of 60° each. Since the sum of the angles in the triangle is 180°, therefore, each angle in the ...
Triangles in complex geometry are extremely nice when they can be placed on the unit circle; this is generally possible, by setting the triangle's circumcircle to the unit circle. This immediately implies the following obvious result: Suppose \(A,B,C\) lie on the unit circle. Then the circumcenter of \(ABC\) is 0.
An isosceles triangle is a triangle that has (at least) two equal side lengths. If all three side lengths are equal, the triangle is also equilateral. Isosceles triangles are very helpful in determining unknown angles. In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle, and the point ...
It consists of 6 equilateral triangles of side length \(R\), where \(R\) is the circumradius of the regular hexagon. The area of the regular hexagon is the sum of areas of these 6 equilateral triangles: \[ 6\times \frac12 R^2 \cdot \sin 60^\circ = \frac{3\sqrt3}2 R^2 .\] Here are examples and problems that relate specifically to the regular ...
Ptolemy's theorem states the relationship between the diagonals and the sides of a cyclic quadrilateral. It is a powerful tool to apply to problems about inscribed quadrilaterals. Let's prove this theorem. We can prove the Pythagorean theorem using Ptolemy's theorem: Submit your answer Once upon a time, Ptolemy let his pupil draw an equilateral triangle ...
