Learning Parallel Lines

Learning parallel lines is very easy. As the name it self indicates that there will be some lines that are parallel to each other. Think logically if two lines are parallel will they ever meet at some point. The answer is no. Because the two parallel lines maintain equal distance between them so there is no chance that they meet at some point. So we can conclude that two lines are parallel if and only if they are coplanar and never meet each other that is they maintain same distance apart.

Transversals are very important while learning parallel lines.

Tranversal can be defined as a line that intersects two or more  lines, at different points. Simply a line that crosses two or more lines  is called transversal. With the help of transversals we can say whether the two given lines are parallel or not. Figure below shows how a transversal looks.



How can we know the lines are parallel or not?

Answer is with the help of some angles that are formed when transversal passes through pair of coplanar lines. These angles are very important while learning parallel lines.The angles are

Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Co-Interior Angles


Corresponding angles:

In our figure the corresponding angles are " a,e " , " d, h" , "b , f" , "c,g".

Alternate Interior angles:

The name it self indicates that alternate means on the other side and interior means inner angles. The Alternate Interior angles are "d,f" and "c,e".

Alternate exterior angles:


The name it self indicates that alternate means on the other side and exterior means outer angles. Alternate exterior angles in the given figure are "a,g" and "b,h".

Co-interior angles:

In the given figure Co-interior interior angles are "d,e" and "c,f".

Now for two lines to be parallel corresponding angles, alternate Interior angles, alternate exterior angles must be equal and sum of Co-interior  angles must be equal to 180. Even if one condition is satisfied it is enough as automatically all the other will satisfy.

This is all about learning parallel lines. Hope you enjoyed it......

Definition of Probability Distribution

Probability distribution function referred as p(x) which is a function that satisfies below properties:

Probability that x can obtain particular value is p(x).

p[X,x]=p(x)=px

p(x) positive for all real x.
Sum of p(x) over all feasible values of x is 1, that is

`sum_(pj)pj=1`

Where, j- all possible values that x can have and pj is probability at xj.

One significance of properties 2,3 is that 0 <= p(x) <= 1.

Steps used for how to determine probability distribution:

Using following steps used to how determine probability distribution:

Step 1 for how to determine probability distribution:

Plot the data for a image illustration of the data type.

Step 2 for how to determine probability distribution:

First steps is to determining what data distribution one has - and thus the equation type to use to model the data - is to rule out what it cannot be.

The data sets cannot be a discrete uniform distribution if there are any crest in the data set.
The data is not Poisson or binomial if the data has more than one crest.
If it contains a single arc, no secondary crests, and contains a slow slope on each side, it may be Poisson or a gamma distribution. But it is not discrete uniform distribution.
If the data is regularly distributed, and it is without a slant in the direction of one side, it is secure to rule out a gamma or Weibull distribution.
If the function has an even distribution or a crest in the center of the graphed outcomes, it is not a geometric distribution or an exponential distribution.
If the incidence of a factor differ with an environmental variable, it probably is not a Poisson distribution.


Step 3 for how to determine probability distribution:

After probability distribution type has been tapering downward, do an R squared examination of each probable type of probability distribution. The one with the maximum R squared value is most possible correct.

Step 4 for how to determine probability distribution:

Remove one outlier data point. Now recalculate R squared. If the same probability distribution form comes up as the neighboring match, then there is high confidence that this is the correct probability distribution to use for group of data.

From above steps we can understand how to use probability distribution.