Download Construction of Geometric Figures: Circles, Line Segments, and Perpendicular Lines and more Essays (high school) Mathematics in PDF only on Docsity!
Mathematics
(Chapter-I14) (Practical Geometry)
(Class- VI)
Exercise 14.
Question 1:
Draw a circle of radius 3.2 cm.
Answer 1: Steps of construction:
(a) Open the compass for the required radius of 3.2 cm.
(b) Make a point with a sharp pencl where we
want the centre of circle to be.
(c) Name ito.
(d) Place the pointer of compasses on 0
(e) Turn the compasses slowly to draw the circle.
.3.2cm
Hence, it is the required circle.
Question 2:
With the same centre O, draw two circles of radii 4 cm and 2.5 cm. Answer 2: Steps of construction:
(a) Marks a point '0 with a sharp pencil where we want the centre of the circle.
(6) Open the compasses 4 cm.
(c) Place the pointer of the compasses on O.
(d) Turn^ the^ compasses slowly to^ draw^ the^ circle (e) Again open the compasses 2.S cm and place the pointer of the compasses on D. (0 Turn the compasses slowly to draw the second circle.
Hence, it is the required fñgure.
4 cm
O 2.
Question 3: Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained ifthe diameters are perpendicular to each other? How do you check our answer? Answer 3; By joining the ends of two diameters, we get a rectangle. By measuring we find AB CD 3 cm, BC =AD = 2 cm, i.e. pairs of opposite sides are equal and also Z A
LB 2C= 2D= 90,, le. each angle is of 90.
Hence, it is a rectangle.
(0)
ne aameters^ are^ perpendicular^
to each other,
then by joining the ends of two diameters, we get
(i)
a square. By measuring we^ find^ that^ AB^ =^ BC^ =^ CD^ =DA^ = 2.5 cm, i.e, all four sides are equal. Also (^) 4A =2B= 2C=^ 2D^ =9. ,Le. each angle is of 9 Hence, it is a square.
QuestionDraw any (^) cirde4: and mark points A, B and C such that
a)Ais on the^ cirde (b) B^ is^ in^ the^ interior^ of^ the^ circle.
() Cis^ in^ the^ exterior^ of the circle.
Answer 4:
Mark a point 'o'^ with^ sharp pencil where^ we^ want^ centre^ of^ the^ circle,
Place the pointer of the compasses at '0'. Then move the compasses slowly to draw a circle.
(a) Point^ A^ is^ on^ the^ circle.
(i)
(6) Point^ B^ is^ in^ interior^ of^ the^ circle (e) Point^ C^ is^ in^ the^ exterior^ of^ the^ circle.
Exercise 14.
Question 1:
Draw a^ line^ segment of^ length^ 7.3^ cm,^ using^ a^ ruler.
L Answerl:
Steps of construction: B 7.3 cm
() Place the zero mark of the ruler at a point A (M) Marka point B at a distance of 7.3 cm from A (11) Joln AB. Hence, AB is the required line segment of length 7.3 cm.
Question 2: Construct a line segment of length 5.6 cm using ruler and compasses
Answer 2:
Steps of construction:
5.6 cm
() Drawa line T'. Mark a point A on this line.
(1) Place the compasses pointer on zero markof the ruler. Open it to place the
(1) pencilWithout^ pointup changing^ to^ 5.6the^ cm opening^ mark of the compasses. Place the pointer on A and
cut an arc 7 at B. AB is the required line segment of length 5.6 cm.
Question 3:
Construct AB^ of^ length^ 7.8^ cm.^ From^ this^ cut^ off^ AC^ of^ length^ 4.7^ cm.^ Measure^ BC
Answer 3: Steps of construction:
A 47 cm
7.8cm-
A 4.7 cm C 3.1 cm B
( Place^ the^ zero^ mark^ of^ the^ ruler^ at^ A. (i) Mark a point B at a distance 7.8 cm from A (i) Again, mark a point C at a distance 4.7 from A.
Hence, by measuring BC, we find that BC 3.1 cm
Question 4:
Given AB of length 3.9 am, construct P such that the length PÙ is twice that of AB
Verily by me asurement
X (^) Q
(Hint: Construct PX such that length of PX = length of AB; then cut off XQ such that XQalso has^ the^ length^ of^ AB. Answer 4 Steps of construction: 3.9 cm
3.9 cm 3.9 cm o
Draw a line T".
(i) Construct PX such that length of PX = length of AB (i) Then cut of XQ such that XQ also has the length of AB. (v) Thus the length of PX and the length of XQ added toge ther make twice the
length of AB
Verification: Hence, by measurement we find that PQ 7.8 cm 3.9 (^) Cm (^) 3.9 cm AB AB =2x AB
Exercise 14. Question 1: Draw any lIne segment PQ. Without measuring PO, construct a copy of PQ. Answer l: Steps of construction:
P-
A
() Given^ PQ^ whose^ length^ is^ not^ known. () Fix the compasses polnter on P and the pencil end on Q The opening of the instrument now gives the length of PQ. (ii) Draw any line ''. Choose a point A on 'T'. Without changing the compasses setting place^ the^ pointer^ on^ A. (iv) Draw^ an^ arc^ that^ cuts^ 'T'^ ata^ point,^ say^ B.
Hence, AB is the copy of PQ.
Question 2:
Given some line segment AB, whose length you do not know, construct PQ such that the length of PQ is twice that of AB. EAnswer 2: Steps of construction:
P R
Given AB whose length is not known.n
(11) Fix the compasses pointer on A and the pencil end on B. The opening of the
instrument now gives the length of AB. (11) Draw any line 7. Choose a point Pon T. without changing the compasses setting place the pointer on Q iv) Draw an arc that cuts T"' ata point R.
( Now^ place^ the^ pointer^ on^ R^ and^ without^ changing^ the^ compasses^ setting draw another arc that cuts "T at a point Q.
Hence, PQ is the required line segment whose length is twice that of AB.
Question 3: Draw a linel and a point X on it. Through X, drawa line segment XY perpendicular to. Now draw^ a^ perpendicular to^ XY^ to^ Y.^ (use^ ruler^ and^ compasse^ s) EL. Answer 3: Steps of construction: Drawa
line T and () with X as centre andtake a convenient^ point^ Xon^ itradius, draw an arc intersecting the line T' at^ two^ points^ A^ and^ B. ii) With A and B as centres and a radius greater than XA, draw two arcs, which cut each other at C. (iv) Join AC and produce it to Y. Then XY is perpendicular to '.
( With D^ as centre^ and^ a^ convenlent
radius, draw an art intersecting XY at
two points C and D. (vi) With C and D as centres and radius greater than YD, draw two arcs which cut each other at F. (vii) Join YF, then YF is perpendicular to XY at Y.
