Rayat Shikshan Sansthas Smt Abbott Highschool Bhingar Smt

Rayat Shikshan Sanstha’s, Smt. Abbott Highschool, Bhingar. • Smt. Salvi Hemlata Vasantrao. • M. Sc. B. ED.

SUB : - MATHS CHAPTER : - 14. CONSTRUCTION OF QUADRILATERALS. Std- 8 Subject-Maths Construction of Quadrilaterals

Introduction 1. Quadrilateral-Has four sides, four angles, four vertices and two diagonals. 2. Unique triangle-Has three sides. 3. Unique Quadrilateral-Has five Parts(four sides In and one of the diagonal or three sides, two diagonals all three sides, two angles etc). 4. Constructionof quadrilaterals. Rectangle, Square, Rombus, Parallelogram, Trapeziu m, Kite. Std- 8 Subject-Maths Constructionof Quadrilaterals

TYPES OF QUADRILATERAL : 1. SQUARE 2. RECTANGLE 3. PARALLELOGRAM 4. RHOMBUS 5. TRAPEZIUM 6. KITE Std- 8 Subject-Maths Constructionof Quadrilaterals

INDEX . To Construct the Quadrilateral given four sides and a iagonal. . To Construct a Quadrilateral given three sides and two iagonal. . To construct a Quadrilateral given two adjacent side and hree angles. . To Construct a Quadrilateral given three sides and two ngles. Std- 8 Subject-Maths Construction of Quadrilaterals

Sub-Unit 1. To Construct the Quadrilateral given four sides and a diagonal. Std- 8 Subject-Maths Construction of Quadrilaterals

Example: 1 CONSTRUCT ABCD SUCH THAT , L [ AB ] = 2. 5 Cm , L [ AD ] = 3. 5 Cm L [ CD ] = 3 Cm , L [BD] = 4. 5 cm, AND L [BC ]=4 CM Std- 8 Subject-Maths Constructionof Quadrilaterals

ROUGH FIGURE : - D M CM A M 3 C C 5. 3 2. 5 4. 5 C CM Std- 8 BSubject-Maths M C 4 Constructionof Quadrilaterals

METHOD / STEPS : 1. 2. 3. 4. 5. 6. 7. 8. EITHER SELECT ONE OF THE FOUR SIDES OR THE DIAGONAL. LET US SELECT THE DIAGONAL BD OF LENGTH 4. 5 CM DRAW DIAGONAL BD OF LENGTH OF 4. 5 CM TAKE' A 'AS CENTRE AND RADIUS OF 2. 5 CM IN YOUR COMPASS OF 2. 5 CM DRAW AN ARC OF ON EITHER SIDE OF DIAGONAL BD. TAKE CENTRE AS D & RADIUS OF 3. 5 CM OUT PREVIOUS ARC. NAME THE INTERSECTING POINT OF THE ARC AS A. SIMILARLY , DRAW POINT C ON THE OPPOSITE SIDE OF THE DIAGONAL BD. THUS ABCD IS THE REQUIED QUADRILATRAL. Std- 8 Subject-Maths Constructionof Quadrilaterals

A 2. 5 3. 5 B 4. 5 CM Std- 8 Subject-Maths D D 4 C CM 4. 5 CM 3 2. 5 CM CM B CM CM 3. 5 A M C Constructionof Quadrilaterals Constructionof

EXERCISE 52 DRAW QUADRILATERAL OF FOLLOWING MEASURE. • 1. IN DEFG l [ DE ] =5 CM , • l [EF ]=6 CM , l [FG ] =7 CM , • l [ DG ]=3 CM , l [ DF ]=9 CM. Std- 8 Subject-Maths Constructionof Quadrilaterals

Sub-Unit 2. To Construct a Quadrilateral given three sides and two diagonal. Std- 8 Subject-Maths Constructionof

EXAMPLE: 2 • CONSTRUCT A QUADRILATERAL NILE such that l(NI)=2. 5 cml, (IL)=3. 5 cm, l(EL)=3 cm, l(NL)=4 cm&l(IE)=5 cm ROUGH FIGURE : - 2. 5 CM I Std- 8 4 C M E 5 CM 3 C M N 3. 5 CM Subject-Maths L Constructionof Quadrilaterals

STEPS : 1. DRAW SEG IL OF LENGTH 3. 5 CM. 2. TAKE' I' AS A CENTRE , RADIUS OF 2. 5 CM DRAW AN ARC. 3. TAKE 'L' AS CENTRE , RADIUS OF 4 CM AND CUT THE PREVIOUS ARC 4. NAME THE INTERESTING POINT OF THE ARC AS POINT N 5. SIMILARALY , OBTAIN THE POINT E AND JOIN POINT N AND POINT F 6. THUS WE GET REQUIRED NILE. Std- 8 Subject-Maths Constructionof

EXERCISE 53 DRAW QUADRILATERAL OF FOLLOWING MEASURE . • IN DEFG l [ EF ] =3. 5 CM , l [ DE ]=5. 5 CM , l [ DF ]= 7. 5 CM , l[ DG ] =5. 5 CM , l [ EG ] =8 CM. Std- 8 Subject-Maths Constructionof Quadrilaterals

N N Std- 8 I Subject-Maths 4 C M 3 CM I L 2. 5 CM 4 C M 3. 5 CM E M C 5 3. 5 CM Constructionof L

Sub-Unit 3. To construct a Quadrilateral given two adjacent side and three angles. Std- 8 Subject-Maths Constructionof

Example: 3 • CONSTRUCT ABCD SUCH THAT l [ AB ]=3 CM , l [ BC ]= 4 CM , • m A=90˚ , m B =65˚ , m C = 110˚ Std- 8 Subject-Maths Constructionof

ROUGH FIGURE : - C D 11 O˚ 4 CM A Std- 8 90˚ 65˚ 3 CM Subject-Maths B Constructionof

STEPS : 1. DRAW SEG AB OF LENGTH 3 CM AS A BASE LINE. 2. DRAW AN ANGLE OF 650 AT VERTEX B 3. TAKE' B' AS CVENTRE , RADIUS OF 4 CM s DRAW AN ARC ON ANGLE AND NAME IT AS 'C'. 4. DRAW AN ANGLE OF 90 ˚ AT POINT A 5. DRAW AN ANGLE 110˚ AT POINT C. 6. THE INTERSECTING OF THE RAYS FROM THE POINT A AND C IS POINT D. 7. THUS WE GET THE REQUIRED ABCD. Std- 8 Subject-Maths Construction of Quadrilaterals

C 4 CM D C 11 O˚ 4 CM 65˚ A 3 CM Std- 8 B Subject-Maths A 90˚ 65˚ 3 CM Constructionof B

EXERCISE 54 DRAW QUADRILATERAL OF FOLLOWING MEASURE . • IN DEFG , l [ DE ] =4. 5 CM , l [ EF ] =6. 5 CM , m D = 65˚ , m E= 100˚ , m F = 60˚. Std- 8 Subject-Maths Constructionof Quadrilaterals

Sub-Unit 4. To Construct a Quadrilateral given three sides and two angles. Std- 8 Subject-Maths Constructionof Quadrilaterals

Example: 4 • CONSTRUCT A PQRS SUCH THAT l [PQ] =3. 5 CM , l[ QR ] =4. 5 CM , l [RS ] =4 CM , m Q = 1100 , m R = 800. Std- 8 Subject-Maths Constructionof Quadrilaterals

Rough figure S 3. 5 CM Q Std- 8 4 CM P 110˚ 80˚ R 4. 5 CM Subject-Maths Construction of Quadrilaterals

STEPS : v SELECT THE SIDE OF THE INCLUDED ANGLE AS SIDE QR OF LENGTH 4. 5 CM AS A BASE LINE. v DRAW AN ANGLE OF MEASURE 800 AT POINT ' R' ON SEGMENT QR. v DRAW RS OF LENGTH 4 CM. v DRAW AN ANGLE OF 1100 AT POINT Q. v DRAW SEGMENT PQ OF LENGTH 3. 5 CM v JOIN POINT P AND S. v PQRS IS THE REQUIRED QUADRILATERAL. Std- 8 Subject-Maths Construction of Quadrilaterals

S 3. 5 CM 110˚ Q Std- 8 4. 5 CM Q 4 CM P P 110˚ R Subject-Maths 80˚ 4. 5 CM Constructionof R

EXERCISE 55 DRAW QUADRILATERAL OF FOLLOWING MEASURE. • IN TYRE , l [ TY ] = 3. 5 CM , l [YR ] =5 CM , l [ RE ] =4. 5 CM , m Y = 60 ˚, m R = 120˚. Std- 8 Subject-Maths Constructionof Quadrilaterals