Dictionary Rank of a Word | Permutations & Combinations

 PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

Triangle Properties And Types Geometry



TRIANGLES ITS PROPERTIES AND TYPES

Triangle:-
A polygon with three sides is called a triangle.

Triangle is a closed figure which have three sides, three angles and three vertices.

Classification of triangles on the bases of sides

These are of three types:-
  • Scalene Triangle
  • Isosceles Triangle
  • Equilateral triangle
Scalene Triangle:- 
A triangle whose all sides are different is called a scalene triangle.

Isosceles Triangle:-
A triangle whose two sides are equal is called isosceles triangle.

Equilateral Triangle:-
A triangle whose all sides are equal is called an equilateral triangle.

Classification of triangles on the basis of angles.
These are of three types:-
  • Acute angled Triangle
  • Right angled Triangle
  • Obtuse angled Triangle 
Acute angled triangle:-
A triangle whose all angles are acute is called acute angled triangle.

Right angled Triangle:-
A triangle whose one angle equal to 90o is called right.

Obtuse angled Triangle:-
A triangle whose one angle is obtuse is called obtuse angled triangle.

Properties of Triangle
  • Sum of all angles of a triangle is equal to 180o.
  • Exterior angle of the triangle is equal to the sum of interior opposite angles.
  • In triangle angles opposite to the equal sides are equal.
  • In triangles angle opposite to the larger side is greater and angle opposite to the smaller side small.
  • A triangle is possible if sum of any two sides is greater than the third side.
  • Difference of two sides < Third side < Sum of two sides.
  • If a line is drawn through the mid points of two sides of triangle then it is parallel to the third side and is half of it.
  • If a line is drawn through the mid point of one side of the triangle and is parallel to the second side then it bisect the third side.
Median of triangle:-
A line segment which join the vertex of the triangle with the mid-point of the opposite side is called median.
  • All medians of the triangle lie inside the triangle.
  • All medians of equilateral triangles are equal.
  • Median divide the triangle into two triangles of equal area.
Centroid of the triangle :-
Point of concurrence of the medians of the triangle is called its centroid.

The point inside the triangle where all the medians meet is called Centroid  of the triangle.

 Centroid of the triangle divide the median  in 2 : 1

Altitudes:-
A Line segment from the vertex of the triangle which is perpendicular on the opposite side is called altitude.

  • Altitudes may be inside or outside of the triangle.
  • Altitude of the acute angled triangle lie inside the triangle.
  • Altitude of right angled triangle lie at the vertex of right angle.
  • Altitude of obtuse angled triangle lie out side the triangle.
  • Altitudes of equilateral triangle are equal.
Orthocenter:-

Point of concurrence of altitudes of the triangle is called orthocenter.

Point at which all the altitudes meet is called orthocenter.

Circumcenter:-
Point of concurrence of perpendicular bisectors of sides of triangle is called Circumcentre and the circle which circumscribe the triangle is called circumcircle .
In-centre :-
Point of concurrence of angle bisectors of the angles of triangle is called In-centre and the circle inside the triangle and touches all the sides is called In-circle.




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