How many possible equivalence classes of triangles might exist given some specific given measures of SSS (side side side) triangle measures in these geometries? a. Euclidean b. Нурerbolic c. Taxicab d. Spherical
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
College Geometry
In Euclidean geometry, if three sides of of two triangles are equal in length, then they are said to be congruent by S-S-S rule.
Let T be the set of all triangles in Euclidean plane. Then the relation congruence by S-S-S rule is an equivalence relation on T
So, in Euclidean geometry, there is one equivalence class of triangles exists given some specific measures of SSS which is
If three pairs of sides of two triangles are equal in length, then they are congruent in hyperbolic plane.
Therefore, in Hyperbolic geometry, there is one equivalence class of triangles exists given some specific measures of SSS which is
Where is the set of all triangles in hyperbolic plane.
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