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![basic maths knowledge - POLYGON Polygon Basics Polygon closed figure with 3 or more sides 2 Types: polygon 180' all diagonals inside Convex all interior angles 7 Concave polygon at least one interior 180', some diagonals outside: ongle 2 Regular Polygon n-sided polygon hqs: Always convex n vertices interior All sides equdl angles All interior gngles equql n exterior qngles. Interior Angles Exterior Angles 2) x 1809 Sum of interior angles (n Sum of all exterior angles = 3609 360 Each interior angle (regular polygon): Each exterior angle (regular polygon): [(n 2) 18091 Internal angle + External angle = 1809 360% Number of sides: n Exterior angle Diagonals 3) Number of diogonols in 0 polygon Regular Hexagon Large diqgonals: FC = AD = BE = 2g Number of sides = 6 Short diagonals: FD BF = V3a 0B Each interior angle = १२०० Regular hexagon = 6 equilateral triangles Each exterior angle 60% Also = 3 rhombus of equql qred Number of diagonals = 9 (3v3/2)q2' Area Perimeter 6a Circumrodius R = 0 Area Relations in Regular Hexagon Triangle EAC is equilateral If P, Q R dre midpoints: APQR is equilateral with side (3a/2) with side V3a Area(EAC) Area(APQR) 2 8 Area(hexagon)| Area(ABCDEF) Regular Octagon] 2(12' Area 1)02 Number of sides = 8 Perimeter 8a Inradius: r = 2v2 _ 2 135% Each interior angle 12+12 . 0 Each exterior angle = ४५९ Circumradius: R = 12 - 12 Number of diagonals = 20 POLYGON Polygon Basics Polygon closed figure with 3 or more sides 2 Types: polygon 180' all diagonals inside Convex all interior angles 7 Concave polygon at least one interior 180', some diagonals outside: ongle 2 Regular Polygon n-sided polygon hqs: Always convex n vertices interior All sides equdl angles All interior gngles equql n exterior qngles. Interior Angles Exterior Angles 2) x 1809 Sum of interior angles (n Sum of all exterior angles = 3609 360 Each interior angle (regular polygon): Each exterior angle (regular polygon): [(n 2) 18091 Internal angle + External angle = 1809 360% Number of sides: n Exterior angle Diagonals 3) Number of diogonols in 0 polygon Regular Hexagon Large diqgonals: FC = AD = BE = 2g Number of sides = 6 Short diagonals: FD BF = V3a 0B Each interior angle = १२०० Regular hexagon = 6 equilateral triangles Each exterior angle 60% Also = 3 rhombus of equql qred Number of diagonals = 9 (3v3/2)q2' Area Perimeter 6a Circumrodius R = 0 Area Relations in Regular Hexagon Triangle EAC is equilateral If P, Q R dre midpoints: APQR is equilateral with side (3a/2) with side V3a Area(EAC) Area(APQR) 2 8 Area(hexagon)| Area(ABCDEF) Regular Octagon] 2(12' Area 1)02 Number of sides = 8 Perimeter 8a Inradius: r = 2v2 _ 2 135% Each interior angle 12+12 . 0 Each exterior angle = ४५९ Circumradius: R = 12 - 12 Number of diagonals = 20 - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_117117_f7fc964_1772115115381_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=381_sc.jpg "basic maths knowledge - POLYGON Polygon Basics Polygon closed figure with 3 or more sides 2 Types: polygon 180' all diagonals inside Convex all interior angles 7 Concave polygon at least one interior 180', some diagonals outside: ongle 2 Regular Polygon n-sided polygon hqs: Always convex n vertices interior All sides equdl angles All interior gngles equql n exterior qngles. Interior Angles Exterior Angles 2) x 1809 Sum of interior angles (n Sum of all exterior angles = 3609 360 Each interior angle (regular polygon): Each exterior angle (regular polygon): [(n 2) 18091 Internal angle + External angle = 1809 360% Number of sides: n Exterior angle Diagonals 3) Number of diogonols in 0 polygon Regular Hexagon Large diqgonals: FC = AD = BE = 2g Number of sides = 6 Short diagonals: FD BF = V3a 0B Each interior angle = १२०० Regular hexagon = 6 equilateral triangles Each exterior angle 60% Also = 3 rhombus of equql qred Number of diagonals = 9 (3v3/2)q2' Area Perimeter 6a Circumrodius R = 0 Area Relations in Regular Hexagon Triangle EAC is equilateral If P, Q R dre midpoints: APQR is equilateral with side (3a/2) with side V3a Area(EAC) Area(APQR) 2 8 Area(hexagon)| Area(ABCDEF) Regular Octagon] 2(12' Area 1)02 Number of sides = 8 Perimeter 8a Inradius: r = 2v2 _ 2 135% Each interior angle 12+12 . 0 Each exterior angle = ४५९ Circumradius: R = 12 - 12 Number of diagonals = 20 POLYGON Polygon Basics Polygon closed figure with 3 or more sides 2 Types: polygon 180' all diagonals inside Convex all interior angles 7 Concave polygon at least one interior 180', some diagonals outside: ongle 2 Regular Polygon n-sided polygon hqs: Always convex n vertices interior All sides equdl angles All interior gngles equql n exterior qngles. Interior Angles Exterior Angles 2) x 1809 Sum of interior angles (n Sum of all exterior angles = 3609 360 Each interior angle (regular polygon): Each exterior angle (regular polygon): [(n 2) 18091 Internal angle + External angle = 1809 360% Number of sides: n Exterior angle Diagonals 3) Number of diogonols in 0 polygon Regular Hexagon Large diqgonals: FC = AD = BE = 2g Number of sides = 6 Short diagonals: FD BF = V3a 0B Each interior angle = १२०० Regular hexagon = 6 equilateral triangles Each exterior angle 60% Also = 3 rhombus of equql qred Number of diagonals = 9 (3v3/2)q2' Area Perimeter 6a Circumrodius R = 0 Area Relations in Regular Hexagon Triangle EAC is equilateral If P, Q R dre midpoints: APQR is equilateral with side (3a/2) with side V3a Area(EAC) Area(APQR) 2 8 Area(hexagon)| Area(ABCDEF) Regular Octagon] 2(12' Area 1)02 Number of sides = 8 Perimeter 8a Inradius: r = 2v2 _ 2 135% Each interior angle 12+12 . 0 Each exterior angle = ४५९ Circumradius: R = 12 - 12 Number of diagonals = 20 - ShareChat")
![english - PRONOUN - TYPES PRONOUN PERSONAL 1. 0ق Used to Definition reploce noun 0 they he, she, it, Examples T, We; you, Object Pronouns Subject Pronouns they him, her, it, them T, We, he, she, it, you, me , US, Jou, POSSESSIVE_PRONOUN 2. Shows_ownership Definition] mine, ours,_yours, his, hers, theirs] Examples న DEMONSTRATTVE PRONOUNAYAYAYAYAYAYAY AYAYAY 3 things | Pointsto_specific_persons Definition] 01 this, that, these, those Examples > REFLEXIVE PRONOUN ^ Refers back to the subject Definition] 8 myself , himself , herself , themselves Examples] ر INTERROGATIVE PRONOUN ss 5. Used to ask questions Definition who, whor , whose, which, what] Examples 6. RELATIVE PRONOUN *~***-**L Definition Joins two clauses ر who, which, that, whose] Examples INDEFINITE PRONOUN @@ @ @ @ @ @@@0@@000 0-0-0 things Refers to_non-specific_persons Definition 0٣ > someone, anyone, everyone, nobody Exomples must agree with the noun in number A pronoun and gender: PRONOUN - TYPES PRONOUN PERSONAL 1. 0ق Used to Definition reploce noun 0 they he, she, it, Examples T, We; you, Object Pronouns Subject Pronouns they him, her, it, them T, We, he, she, it, you, me , US, Jou, POSSESSIVE_PRONOUN 2. Shows_ownership Definition] mine, ours,_yours, his, hers, theirs] Examples న DEMONSTRATTVE PRONOUNAYAYAYAYAYAYAY AYAYAY 3 things | Pointsto_specific_persons Definition] 01 this, that, these, those Examples > REFLEXIVE PRONOUN ^ Refers back to the subject Definition] 8 myself , himself , herself , themselves Examples] ر INTERROGATIVE PRONOUN ss 5. Used to ask questions Definition who, whor , whose, which, what] Examples 6. RELATIVE PRONOUN *~***-**L Definition Joins two clauses ر who, which, that, whose] Examples INDEFINITE PRONOUN @@ @ @ @ @ @@@0@@000 0-0-0 things Refers to_non-specific_persons Definition 0٣ > someone, anyone, everyone, nobody Exomples must agree with the noun in number A pronoun and gender: - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_467604_160b3207_1772085466256_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=256_sc.jpg "english - PRONOUN - TYPES PRONOUN PERSONAL 1. 0ق Used to Definition reploce noun 0 they he, she, it, Examples T, We; you, Object Pronouns Subject Pronouns they him, her, it, them T, We, he, she, it, you, me , US, Jou, POSSESSIVE_PRONOUN 2. Shows_ownership Definition] mine, ours,_yours, his, hers, theirs] Examples న DEMONSTRATTVE PRONOUNAYAYAYAYAYAYAY AYAYAY 3 things | Pointsto_specific_persons Definition] 01 this, that, these, those Examples > REFLEXIVE PRONOUN ^ Refers back to the subject Definition] 8 myself , himself , herself , themselves Examples] ر INTERROGATIVE PRONOUN ss 5. Used to ask questions Definition who, whor , whose, which, what] Examples 6. RELATIVE PRONOUN *~***-**L Definition Joins two clauses ر who, which, that, whose] Examples INDEFINITE PRONOUN @@ @ @ @ @ @@@0@@000 0-0-0 things Refers to_non-specific_persons Definition 0٣ > someone, anyone, everyone, nobody Exomples must agree with the noun in number A pronoun and gender: PRONOUN - TYPES PRONOUN PERSONAL 1. 0ق Used to Definition reploce noun 0 they he, she, it, Examples T, We; you, Object Pronouns Subject Pronouns they him, her, it, them T, We, he, she, it, you, me , US, Jou, POSSESSIVE_PRONOUN 2. Shows_ownership Definition] mine, ours,_yours, his, hers, theirs] Examples న DEMONSTRATTVE PRONOUNAYAYAYAYAYAYAY AYAYAY 3 things | Pointsto_specific_persons Definition] 01 this, that, these, those Examples > REFLEXIVE PRONOUN ^ Refers back to the subject Definition] 8 myself , himself , herself , themselves Examples] ر INTERROGATIVE PRONOUN ss 5. Used to ask questions Definition who, whor , whose, which, what] Examples 6. RELATIVE PRONOUN *~***-**L Definition Joins two clauses ر who, which, that, whose] Examples INDEFINITE PRONOUN @@ @ @ @ @ @@@0@@000 0-0-0 things Refers to_non-specific_persons Definition 0٣ > someone, anyone, everyone, nobody Exomples must agree with the noun in number A pronoun and gender: - ShareChat")
![grammer - ADJECTIVE 6. [DEMONSTRATIVE ADJECTIVE BASIC DEFINITION 1 Points out noun Adjective A word that describes] This book, Those Examples apples qualifies Or q noun. POSSESSIVE_ADJECTIVE 7. Tall boy, Red pen; Examples Shows ownership Honest man bag My pen, His Examples TYPES OF ADJECTIVE 2 8. [INTERROGATIVE ADTECTIVE Adjective of Quality ask question Used to Adjective of Quantity Which book? What time? Examples Adjective of Number DEGREES OF ADJECTIVE 9 Demonstrative Adjective Possessive Adjective Tall Positivel Tnterrogative Adjective Taller Comparative Superlative Tallest ADJECTIVE OF QUALITY 3 A SENTENCE 10.ADJECTIVE IN quality kind Shows Or She is clever girl. Good, Bod, Honest Examples [ADJECTIVE_OF_QUANTITY TMPORTANT SHORTCUTS 11. Adjective describes Shows amount noun Comes before Much, Little, Some generally Examples noun of adjective form No plurall 5. ADJECTIVE OF NUMBER 12. COMMON MISTAKES X Shows number or order X She is smarter more One, Two, First Examples She is smarter boys X These kind of boys This kind of 13.QUICK REVISION BOX Describing word Adjective important] Types are Very usefull for exams ADJECTIVE 6. [DEMONSTRATIVE ADJECTIVE BASIC DEFINITION 1 Points out noun Adjective A word that describes] This book, Those Examples apples qualifies Or q noun. POSSESSIVE_ADJECTIVE 7. Tall boy, Red pen; Examples Shows ownership Honest man bag My pen, His Examples TYPES OF ADJECTIVE 2 8. [INTERROGATIVE ADTECTIVE Adjective of Quality ask question Used to Adjective of Quantity Which book? What time? Examples Adjective of Number DEGREES OF ADJECTIVE 9 Demonstrative Adjective Possessive Adjective Tall Positivel Tnterrogative Adjective Taller Comparative Superlative Tallest ADJECTIVE OF QUALITY 3 A SENTENCE 10.ADJECTIVE IN quality kind Shows Or She is clever girl. Good, Bod, Honest Examples [ADJECTIVE_OF_QUANTITY TMPORTANT SHORTCUTS 11. Adjective describes Shows amount noun Comes before Much, Little, Some generally Examples noun of adjective form No plurall 5. ADJECTIVE OF NUMBER 12. COMMON MISTAKES X Shows number or order X She is smarter more One, Two, First Examples She is smarter boys X These kind of boys This kind of 13.QUICK REVISION BOX Describing word Adjective important] Types are Very usefull for exams - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_688329_cbac55a_1772035623891_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=891_sc.jpg "grammer - ADJECTIVE 6. [DEMONSTRATIVE ADJECTIVE BASIC DEFINITION 1 Points out noun Adjective A word that describes] This book, Those Examples apples qualifies Or q noun. POSSESSIVE_ADJECTIVE 7. Tall boy, Red pen; Examples Shows ownership Honest man bag My pen, His Examples TYPES OF ADJECTIVE 2 8. [INTERROGATIVE ADTECTIVE Adjective of Quality ask question Used to Adjective of Quantity Which book? What time? Examples Adjective of Number DEGREES OF ADJECTIVE 9 Demonstrative Adjective Possessive Adjective Tall Positivel Tnterrogative Adjective Taller Comparative Superlative Tallest ADJECTIVE OF QUALITY 3 A SENTENCE 10.ADJECTIVE IN quality kind Shows Or She is clever girl. Good, Bod, Honest Examples [ADJECTIVE_OF_QUANTITY TMPORTANT SHORTCUTS 11. Adjective describes Shows amount noun Comes before Much, Little, Some generally Examples noun of adjective form No plurall 5. ADJECTIVE OF NUMBER 12. COMMON MISTAKES X Shows number or order X She is smarter more One, Two, First Examples She is smarter boys X These kind of boys This kind of 13.QUICK REVISION BOX Describing word Adjective important] Types are Very usefull for exams ADJECTIVE 6. [DEMONSTRATIVE ADJECTIVE BASIC DEFINITION 1 Points out noun Adjective A word that describes] This book, Those Examples apples qualifies Or q noun. POSSESSIVE_ADJECTIVE 7. Tall boy, Red pen; Examples Shows ownership Honest man bag My pen, His Examples TYPES OF ADJECTIVE 2 8. [INTERROGATIVE ADTECTIVE Adjective of Quality ask question Used to Adjective of Quantity Which book? What time? Examples Adjective of Number DEGREES OF ADJECTIVE 9 Demonstrative Adjective Possessive Adjective Tall Positivel Tnterrogative Adjective Taller Comparative Superlative Tallest ADJECTIVE OF QUALITY 3 A SENTENCE 10.ADJECTIVE IN quality kind Shows Or She is clever girl. Good, Bod, Honest Examples [ADJECTIVE_OF_QUANTITY TMPORTANT SHORTCUTS 11. Adjective describes Shows amount noun Comes before Much, Little, Some generally Examples noun of adjective form No plurall 5. ADJECTIVE OF NUMBER 12. COMMON MISTAKES X Shows number or order X She is smarter more One, Two, First Examples She is smarter boys X These kind of boys This kind of 13.QUICK REVISION BOX Describing word Adjective important] Types are Very usefull for exams - ShareChat")
![english - SIMPLE PRESENT 66 99 TENSES DEEINITION is_used_to expze8s_daily Simple_Pnesent_Tense ond_urivexsal_tuuths Jacts habits genenal] తసగ STRUCTURE ठ Allimative Sentence + $ |es_Iox_thixud_pextson) V Subject + plus_Cucket: Example She Sentencel Negative do not | does not + Vi Subject + ply_cicket does not Example] Shel Intలuoqoovs Sentence V ? Subject Do _ Pu Cucket ? Example Does he TIME EXPRESSIONS-<S USES usually , Doitts always , Aoutines oten; dilu' ) day eveu Genexol Jacts Univexsal tuths Example Ihe sun xisesin theeast PRESENT with thiid petson sinqulat (he, she,it) Use $ |es SIMPLE PRESENT 66 99 TENSES DEEINITION is_used_to expze8s_daily Simple_Pnesent_Tense ond_urivexsal_tuuths Jacts habits genenal] తసగ STRUCTURE ठ Allimative Sentence + $ |es_Iox_thixud_pextson) V Subject + plus_Cucket: Example She Sentencel Negative do not | does not + Vi Subject + ply_cicket does not Example] Shel Intలuoqoovs Sentence V ? Subject Do _ Pu Cucket ? Example Does he TIME EXPRESSIONS-<S USES usually , Doitts always , Aoutines oten; dilu' ) day eveu Genexol Jacts Univexsal tuths Example Ihe sun xisesin theeast PRESENT with thiid petson sinqulat (he, she,it) Use $ |es - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_415650_cf609c_1772011395520_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=520_sc.jpg "english - SIMPLE PRESENT 66 99 TENSES DEEINITION is_used_to expze8s_daily Simple_Pnesent_Tense ond_urivexsal_tuuths Jacts habits genenal] తసగ STRUCTURE ठ Allimative Sentence + $ |es_Iox_thixud_pextson) V Subject + plus_Cucket: Example She Sentencel Negative do not | does not + Vi Subject + ply_cicket does not Example] Shel Intలuoqoovs Sentence V ? Subject Do _ Pu Cucket ? Example Does he TIME EXPRESSIONS-<S USES usually , Doitts always , Aoutines oten; dilu' ) day eveu Genexol Jacts Univexsal tuths Example Ihe sun xisesin theeast PRESENT with thiid petson sinqulat (he, she,it) Use $ |es SIMPLE PRESENT 66 99 TENSES DEEINITION is_used_to expze8s_daily Simple_Pnesent_Tense ond_urivexsal_tuuths Jacts habits genenal] తసగ STRUCTURE ठ Allimative Sentence + $ |es_Iox_thixud_pextson) V Subject + plus_Cucket: Example She Sentencel Negative do not | does not + Vi Subject + ply_cicket does not Example] Shel Intలuoqoovs Sentence V ? Subject Do _ Pu Cucket ? Example Does he TIME EXPRESSIONS-<S USES usually , Doitts always , Aoutines oten; dilu' ) day eveu Genexol Jacts Univexsal tuths Example Ihe sun xisesin theeast PRESENT with thiid petson sinqulat (he, she,it) Use $ |es - ShareChat")
