Scalene triangle

Because no sides are marked as congruent in this figure, the classification by sides is scalene. There is one angle greater than 90° (angle b is 105°) therefore, the angle classification is obtuse. This triangle is obtuse scalene. 

Scalene Triangle no equal sides Isosceles Triangle at least two equal sides Equilateral Triangle all sides equal... 

We conclude with an alternative view of prochirality n> which is based on chirality in two dimensions. A scalene triangle, or any triangle with three differently labeled vertices A, B, C exists in two-dimensional mirror images, as shown in Fig. 76. 

You can classify triangles into three categories based on the number of equal sides. Scalene Triangle no equal sides... 

All the methods presented above are based on the same principle i.e., the material balance using the lever rule. Therefore these are not limited to equilateral triangles, but equally valid for scalene triangles which frequently appear when dealing with subsystems. 

Figure 1. Chiral figures in the plane (m = mirror line). Top enantiomorphous scalene triangles. Bottom enantiomorphous oriented circles.

The chirality of objects such as scalene triangles and oriented circles in R2 (Figure 1) and helices in R3 (Figure 3) is a property shared by both enantiomorphs the difference between them is their sense of chirality. In what follows, we shall for simplicity use the term configuration to stand for sense of chirality. Two enantiomorphs are thus said to have opposite configurations. 

To conclude this chapter, we present the quantum mechanical results of the particle-in-a-triangle problem. Before going into details, we first need to note that, if the box is a scalene triangle, no analytical solution is known. Indeed, the Schrodinger equation is exactly solvable for only a few triangular systems. In addition, for all these solvable (two-dimensional) cases, the wavefunctions are no longer the simple products of two functions each involving only one variable. 

The asymmetric tetrahedron with unlabeled vertices is the three-dimensional analog of the unlabeled scalene triangle. While conversion of such a tetrahedron to its enantiomorph by way of an achiral tetrahedron is certainly not excluded, as illustrated in Fig. 2 for interconversion by way of a Cj-symmetric intermediate, achiral pathways are easily circumvented because the set of achiral unlabeled tetrahedra in E, unlike the set of achiral unlabeled triangles in E, does not form a boundary between heterochiral sets. 

Scalene triangles have no sides that are congruent. 

All of the angles are acute, and all are different. Therefore, the triangle is acute scalene, choice a. 

Fig. 2.9. Linear triatomic molecules interchange of the central atom with a terminal one by bending through a series of scalene triangles into an equilateral triangle and then straightening out again. The two alternative modes of bending lead to two families of scalene triangles that are isometric in pairs but not superimposable in two dimensions...

The construction can be extended to other symmetries by adapting the shape of the net. Cylindrical fullerenes with a fivefold rotational axis have nets consisting of 10 equilateral and 10 scalene master triangles arranged in five parallel strips, specified by a set of four integers the net of a sixfold cylinder can be produced from the same code if an extra parallel strip is added. The cylindrical fullerenes C have... 

Tetrahedral(r+ = 7), T, and T) fullerenes can be constructed from a net based on the general twisted, truncated tetrahedron that has two sets of 4 equilateral and 12 scalene master triangles. Again, only four integers, with appropriate restrictions, are needed to code the structure. The vertex counts of the T+ C fullerenes are ... 

In AR theory (as well as in distillation theory), the region of concentrations that obey mass balance constraints is often referred to as the mass balance triangle— this is because S takes the shape of a scalene or right-angled triangle in and a tetrahedron in We prefer to use the term stoichiometric subspace , however, as S is not always represented by these shapes, particularly for unusual reaction stoichiometry. 

Definition 20. Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal. 

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