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

CONGRUENCE OF TRIANGLES

CONGRUENCE OF TRIANGLES
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CONGRUENCE OF TRIANGLES

CONGRUENT FIGURES:- 

Two  figures are said to be congruent if its all parts are equal. That is their all angles and all sides are equal.

CONGRUENCE OF TRIANGLES :-


Two triangles are congruent if their all sides and all angles are equal. 
The main Congruence conditions are as follows:-
1) Side-Side-Side Congruence condition
2) Side-Angle-Side Congruence rule
3) Angle-Side-Angle Congruence rule
4) Angle-Angle-Side Congruence rule
5) Right angle-Hypotenuse-One side Congruence rule
CONGRUENCE OF TRIANGLES

Explanation of each rule of congruency of triangles

1) Side-Side-Side Congruence condition(SSS ≅ Rule):- 

If three sides of one triangle are  equal to the corresponding three sides of other triangle then triangles are said to be congruent and the condition is called SSS ≅ condition.


      In ABC and DEF
                AB = DE
               BC = EF
               AC = DF
∴ by SSS ≅ rule ABC ≅  DEF

2) Side-Angle-Side Congruence rule(SAS ≅ Rule):-

 If two sides and included angle of one triangle are  equal to the corresponding two sides and included angle of other triangle then triangles are said to be congruent and the condition is called SAS ≅ condition.



   In ABC and DEF
            AB = DE
            AC = DF
            ∠A = ∠D
∴ by SAS ≅ rule ABC  DEF


CONGRUENCE OF TRIANGLES

3) Angle-Side-Angle Congruence rule:- 

If two angles and included side of one triangle are  equal to the corresponding two angles and included side of other triangle then triangles are said to be congruent and the condition is called ASA ≅ condition.   


     In ABC and DEF
         ∠B = ∠E
         BC = EF
         ∠C = ∠F
∴ by ASA ≅ rule ABC  DEF

4) Angle-Angle-Side Congruence rule:- 

If two angles and one side of one triangle are  equal to the corresponding two angles and one side of other triangle then triangles are said to be congruent and the condition is called    AAS≅ condition.                          

         In ABC and DEF
                ∠A = ∠D
                ∠B = ∠E
                BC = EF


by AAS ≅ rule ABC  DEF
CONGRUENCE OF TRIANGLES

5) Right angle-Hypotenuse-One side Congruence rule:- 

In Right angled triangles if hypotenuse and one side of one triangle are respectively equal to the corresponding hypotenuse and one side of other triangle then triangles are congruent and the condition is called RHS ≅ condition.


In ABC and DEF
    ∠C = ∠F.....(each = right angle
    AB = DE
    AC = DF
by RHS ≅ rule ABC  DEF


CONGRUENCE OF TRIANGLES

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