Loading [MathJax]/jax/output/HTML-CSS/jax.js

SChand CLASS 9 Chapter 11 Rectilinear Figures Exercise 11(D)

 Exercise 11 D

Question 1

Sol: (i) Draw a line segment BC=5.2cm
 (ii) At B draw a ray BX making an angle of 45 and cut off BA=6.5cm
(iii) With center C and radius 6.5cm and with center A and radius 5.2 cm, draw arcs intersecting each other at D.
 (iv) Join AD and CD 
ABCD is the required ||gm
(IMAGE TO BE ADDED)

Question 2

Sol:(i)Draw diagonal BD =6.8 cm and bisect it at O.
(IMAGE TO BE ADDED)
(ii) From O, Draw a ray OX making an angle of 60 and  product 
(iii) Cut of OA = OC =4.4\2= 2.2cm
(iv) Join AB, BC , CD and DA 
ABCD is the required ||gm

Question 3

 Sol:(i) Draw a line segment AB=6cm
(ii) At A , draw a perpendicular AX and Cut off AP =2.9cm
(iii) From P, and EPF ||AB
(iv) With center B and A and radius 4cm draw arcs cutting EF at D and C.
(v) Join AD and BC.
Then ABCD is the required ||gm
 (IMAGE TO BE ADDED)

Question 4

Sol:(i) Draw a line segment AB=4.3cm
(ii) At B draw a ray BY. 
(iii) At A, draw perpendicular AX and Cut off AE =3cm
(iv) From E draw a parallel line to AB which Intersects By at C.
(v)With center A and radius BC, draw an arc cutting EF at D.
(vi) Join AD.
Then ABCD is the required ||gm
 (IMAGE TO BE ADDED)
 
Question 5

Sol: (i)Draw a line segment AB=6 cm
(ii) At A draw a ray AX making an angle of 45 and cut off AD=3 cm.
(iii)With center B and Radius 3cm and with center D and Radius 6cm, Draw arcs intersecting each other at C.
(iv) Join BC and DC 
ABCD is the required ||gm
(v) Draw the angle bisector of A meeting CD at P and join BP
 (IMAGE TO BE ADDED)

To prove: APB=90
proof: In ADB
DPA=PAB
But DAP=PAB
DAP=BPA=452=2212
AD=DO=3 cm
Similarly in BCP
PC=DCDP=63=3 cm
So PC=CB=3 cm
So CPB=CBP
But CPB+CBP=180BCP
=18045=135
CPB=CBP=1392=6712
But DPA+CPB+APB=180
2212+6712+APB=180
=90+APB=180
APB=18090=90
Hence APQ=90

Question 6

Sol: The diagonal AC and BD of a ||gm ABCD bisect each other 
AO=OC=102=5 cm
and BO=OD=62=3 cm

(i) Draw a line segment AB =4cm 
(ii) With center a and radius 5cm and with center B and radius 3cm draw which intersect each other at O. 
(iii) Join OA and OC.
(iv) Produce AO to C such that Ao=OC  and produce BO to B such that BO=OD 
(v) Join AD, DC ,CB
Then ABCD is the required ||gm

Question 7

Sol: (i) Draw a line segment AC =10cm and bisect it at O.
(ii) AT O, Draw a ray OX making an angle of 60 and produce XO to Y. 
(iii) From O, cut off OD = OB = 62=3 cm
(iv) Join AB,BC , CD and DA. 
ABCD is the required ||gm

Whose longer side is BC or AD on measuring it , it is 6cm long. 
(IMAGE TO BE ADDED)

Question 8

Sol;(i) Draw a line AX.
(ii) AT A, Draw a perpendicular and cut off AL = 3cm 
(iii) Through L draw LY parallel to AX.
(iv) From A, Draw a ray making an angle of 60 which meets LY at D. 
(v) AT AD. draw a perpendicular and cut off AM = 4cm
(vi) Through M, draw a line parallel to AD which Meets LY at C. 
Then ABCD is the required parallelogram 
(IMAGE TO BE ADDED)

Question 9

Sol: If diagonal of a ||gm bisect each other 
AO=OC and OB =OD = 2.5cm
Steps of construction :
(i) Draw a line segment AC=7cm and bisect it at O. 
(ii) AT O. draw a line making an angle of 75 and produce it to both sides
(iii) From O, Cut off OB =OD =52=2.5 cm. 
(iv) Join AB, BC, CD and DA 
ABCD is the required ||gm
Measuring its shorter side AD=4cm 
(IMAGE TO BE ADDED)

Question 10

Sol: (i) Draw a line segment AB = 3.6cm
(ii) AT, A draw a ray AX making an angle of 45 and cut off AB=3.6cm
(iii)With center B and D and radius 3.6cm draw arcs intersecting each other at C.
(iv) Join BC and CD 
Then ABCD is the required rhombus 
(IMAGE TO BE ADDED)


Question 11

Sol: (i) Draw a line segment AB =3.2cm
(ii) AT A and B draw perpendiculars AX and BY and Cut off AD = BC =3.2cm
(iii) Join DC 
ABCD is the required Square 
(iv) Join its diagonals AC and BD 
On Measuring each =4.5 cm and each angles between these diagonals is 90 AOB=90
(IMAGE TO BE ADDED)

Question 12

Sol: We know that diagonals of a square bisect each other at right angles and diagonals are also equal 
Steps of construction: 
(i) Draw a line segment PR =5cm and draw its perpendicular bisects XY intersecting it at O.
(ii)Cut off OQ = OS =52=2.5 cm
(iii) Join PQ, QR, RS and SP respectively. 
Then PQRS is the required square on measuring its side PQ which is = 3.6cm

(IMAGE TO BE ADDED)

Question 13

Sol: Steps of construction: 
(i) Draw a line segment AB = 4.2 cm 
(ii)AT A and B, Draw perpendicular AX and BY 
(iii) Join CD
Then ABCD is the required rectangle 

(IMAGE TO BE ADDED)

Question 14

Sol: Diagonals of a rectangle bisect each other and arc equal in length 
Steps of Construction: 
(i) Draw a line segment AC = 6cm
(ii) Bisect AC and O. 
(iii) From O, draw a line XY 
Making an angle of 37 and produce it to both side of O.
(iv) From XY Cut off OC =OD = 3cm
 (v) Join AB, BC , CD and AD,
Then ABCD is the required rectangle.

(IMAGE TO BE ADDED)

Question 15

Sol: The diagonals of a square bisect each other at right angles and arc also equal in length. 
Steps of Construction: 
(i) Draw a line segment AC =5cm
(ii) Draw its perpendicular bisector XY intersecting at O. 
(iii) Cut off OB =OD =2.5CM
(iv) Join AB, BC, CD and DA respectively 
Then ABCD is the required square
On measuring its side it is 3.6 cm each 


(IMAGE TO BE ADDED)

Question 16

Sol: Diagonals of rectangle bisect each other and are equal to each other in length.
Steps of constructions:
(i) draw a line segment AC=6 cm and bisect it at O .
(ii)At O , draw a line XY making an angle of 45 and produce it to both of O .
(iii) cut off OB=OD=62=3 cm.
(iv)Join AB, BC, CD and DA respectively
Then ABCD is the required rectangle. 
(IMAGE TO BE ADDED)

Question 17

SoL: Diagonals of a rhombus bisect each other at right angles.

Steps of constructions:
(i) Draw a line segment PR=8 cm
(ii) Draw its perpendicular bisector XY which intersects PR at 0 .
(iii) from XY act off OQ=OS=62=3 cm.
(iv) Join PQ,QR,RS and SP
Then PQRS is the required rhombus 
(IMAGE TO BE ADDED)

(v) if the required point X is equidistant rom p and PS.
So it lies on the angle bisectors of LQPS which is the diagonal PR

it is equidistant from R and S

 Then it will be on the perpendicular bisector of ks Now draw perpendicular bisector of RS which intersects PR at X

Then X is the required point 
Construction the trapezium PQRS in which PQ is parallel to RS from the given measurement in problem 18 to 20 without using set square and protractor as far as possible

Question 18

Sol:  Steps of constructions:
(i) Draw a line segment PQ=7 cm.
(ii) Take a point E such that AE =SR = 2.5 cm and then EQ = 7 -2.5 =4.5cm
(iii) With center E and radius 3cm and with center Q and radius 3.5cm Draw arcs which intersect each other at R 
(iv)Join ER and QR.
(v)with conter R and radius 2.5 cm and with center P and radius 3 cm draw arcs intersecting each other at S .
 (vi) Join RS and PS.
Then PQRS is the required trapezium 
(IMAGE TO BE ADDED)

Question 19

Sol: Steps of constructions:
(i) draw a line segment PQ=8 cm.
(ii) cut off PE=RS=3 cm.
(iii) With center E and Radius 2cm and with center    Q and radius 4cm draw intersecting each other at R. 
(IV) Join ER and QR
(v) with center P and radius 2 cm and with conter R and radius 3 cm draw arcs intersecting each other at S.
(vi) Join PS and SR.
Then PQRS is the required trapezium On measuring the angle QPS it is 50
(IMAGE TO BE ADDED)

Question 20

Sol:if ABC=120 and ABDC
 So BCD=180120=60

(i) draw a line segment AB=4 cm
(ii) AT B draw a ray BX making an angle of 120 and cut off BC = 2.5cm
(iii) At c draw and the ray CY making an angle of 60
(iv) with centre A and radius 2.4 cm draw an are which intersects CY at D and O

If A is obtuse and by joining AD then angle 
So Join AD 
Then ABCD is the required trapezium on measuring AC it is 5.5cm
(IMAGE TO BE ADDED)

Question 21

(i) draw a line segment AB=6.5 cm
(ii)produce it to P such that- BP =3 cm
(iii)with conter p and radius 5 cm and with center A and radius 7 cm draw ares which intersect each other at C
(iv) Join AC and PC and BC.
(v)With conter B and recdius 5 cm and with conter c and radius 3 cm, draw ares intersecting each other at D.
(vi) Join AD , BD and CD 
Then ABCD is the required trapezium.
(IMAGE TO BE ADDED)

Question 22

Sol: The radius of the circumcircle al a regular hexagon is the length of the side of the regular hexagon.
(i) Draw a circle with center O and radius 4cm
(ii) Take a point A on it and from A, draw ars of 4 cm cutting the circle at B,C,D, F and F.
(iii) Join AD,BC,CD,DE,EF and FA.
(IMAGE TO BE ADDED)

Then ABCDEF is the required regular h exagon The area ag regular hexagon =6×34( side )2
=634(4)2
=6×3×164=243 cm2
=24(1.732)cm2
=41.568 cm2

Question 23

Sol; The radius of the circumcircle of a regular hexagon is the length of the side of this hexagon. 
(i) Draw a circle with center O and radius 3.2cm
(ii)Take a point A on the circle 
(iii) Start from A and Radius 3.2cm the arcs on the circle at B,C,D E and F
(IV) Join AB, BC , CD , DE , EF and FA 
Then ABCDEF is required regular hexagon 
(IMAGE TO BE ADDED)

No comments:

Post a Comment

Contact Form

Name

Email *

Message *