Points of concurrency in triangles

There are 3 types of concurrency in triangles.

The centre of these concurrencies are  named   Incentre, circumcentre and orthocenter.

The incenter  helps in forming the in circle in a triangle

The circumcentre is used to circumscribe a triangle.

Incentre:-

The internal bisectors of the three vertical angles are concurrent. This point of concurrency is called Incenter.

I is the Incentre,

I is found  using the formula (ax1+bx2+cx3) / (a+b+c) and  (ay1+ by2+ cy3)/( a+b+c)

 'a' is the side opposite vertex A, 'b' is the side opposite vertex B and  'c' is the side opposite vertex C.

Circumcentre, a Point of Concurrency in Triangles

The perpendicular bisectors of the sides of a triangle are  concurrent. This point of concurrency is called  Circumcenter, and is denoted by the letter S.

The circumcenter is the centre of the circle passing through the 3 vertices  A, B and C

To find S first we find the midpoint of one side of the triangle.  Let us find the midpoint of AB.

Then let us find the slope of AB.

Using slope - one point formula, we can find the circumcenter.

Orthocentre, a Point of Concurrency in Triangles

The altitudes of a triangle are concurrent. This point of concurrency is called orthocenter.  Its symbol is O.

Orthocenter is also found using slope of altitude, one point(coordinate) formula.

For the 2 altitudes we find the equations and then solve the equations.

we must find slope of AD and  use the coordinates of A to find the equation of AD.

Then we must find slope of BE , use the coordinates of B to find the equation of BE'

The solve both equations o AD and BE to get the orthocenter O.

Noun and its Types

Parts of speech are one of the most important lessons in English that every kid needs to understand to get started with the language. There are eight parts of speech – Noun, Pronoun, Verb, Adjective, Adverb, Preposition, Conjunction and Interjection. Noun is the part of speech that refers to a concrete entity. Nouns can be names of people, objects, places or an idea. For example: Ram bought Barbie dolls for his kid. (Ram is a noun). Where is America? (America is a noun). There are two basic types of nouns – Common noun and Proper noun. Further, there are Concrete nouns and Abstract noun.

Common noun: A common noun is the name of a general person, place, thing or an idea. It is not specific to a particular thing. For example: Toys of Fisher Price brand are of great quality. Here, ‘toys’ is a common noun. Cats love drinking milk. Here, ‘cats’ is a common noun.

Proper noun: A proper noun is the name of a specific person, place, thing or an idea. Unlike common noun, it is specific to a particular thing. For example: Tina loves to play with Barbie dolls. Here, ‘Tina’ is a proper noun. Peter is playing with angry birds toys. Here, ‘Peter’ is a proper noun.

Concrete noun: A concrete noun is a type of noun that refers to senses and the ability to hear, touch, feel, smell or taste. For example: Water doesn’t have any color. Here, ‘water’ is a concrete noun. Father bought chair for his kid from Fisher Price brand. Here, ‘chair’ is a concrete noun.

Abstract noun: An abstract noun as the term suggests is a noun form that refers to abstract objects such as ideas or concepts. For example: The judge has given justice. Here, ‘justice’ is an abstract noun. Everyone has their own responsibilities. Here, responsibility is an abstract noun.

These are the basic classifications of nouns. Nouns can also be classified as countable nouns and uncountable nouns. Countable nouns as the term suggests have a singular or plural form while on the other hand uncountable nouns can exist only in singular. Examples of countable nouns are: friends, angry bird toys, houses etc. are countable nouns. Examples of uncountable nouns are: money, bread, etc. These are the different types of nouns that a kid needs to realize in order to get started with the English language.