exercise 13 - testlabz · diagram to make it symmetric. ans. the complete diagram is as under :...

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13 SYMMETRY

Exercise 13.1

Q.1. List any four symmetrical objects from your home or school.

Ans. (i) Tube light (ii) Table top (iii) Computer disc (iv) Blackboard

Q.2. For the given figure, which one is the mirror line l1 or l2?

Ans. When we fold the figure along l1 the parts of the figure do

not coincide, but when we fold the figure along l2 the equal parts coincide to each other. Therefore, l2 is the mirror line.

Q.3. Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well.



Ans. Figure (a), (b), (d), (e) and (f) are symmetric and the line of symmetry is drawn as a dotted line given below.

Figure (c) is not symmetric because it has no line of

symmetry. Q.4. Copy the following on a squared paper. A square paper

is what you would have used in your arithmetic note book in earlier classes. Then complete them such that the dotted line is the line of symmetry.

Ans. Keeping the dotted line as the line of symmetry and

completing the figure, we have



Q.5. In the figure, l is the line of symmetry. Complete the

diagram to make it symmetric.

Ans. The complete diagram is as under :

Q.6. In the figure, l is the line of symmetry. Draw the image

of the triangle and complete the diagram so that it becomes symmetric.



Ans. The image of the triangle is shown such that the complete diagram becomes symmetric.

Exercise 13.2

Q.1. Find the number of lines of symmetry for each of the following shapes :



Ans. Each one of the given figures are symmetrical about the dotted line(s) drawn. The number of lines of symmetry are indicated against each figure.

Q.2. Copy the triangle in each of the following figures on

squared paper. In each case, draw the line(s) of symmetry, if any and identify the type of triangle. (Some



of you may like to trace the figures and try paper-folding first!)

Ans. (a), (b) and (d) are isosceles triangle and (c) is right

isosceles triangle. The lines of symmetry are :

Q.3. Complete the following table. Shape Rough figure Number of lines of symmetry Equilateral triangle 3 Square Rectangle



Isosceles triangle Rhombus Circle Ans. Shape Rough figure Number of lines of symmetry Equilateral triangle 3

Square 4



Rectangle 2

Isosceles Δ 1 Rhombus 2 Circle Infinite

Q.4. Can you draw a triangle which has (a) exactly one line of symmetry? (b) exactly two lines of symmetry? (c) exactly three lines of symmetry? (d) no lines of symmetry? Sketch a rough figure in each case.

Ans. (a) Yes, we can draw an isosceles triangle which has exactly one line of symmetry.

(b) No, we can not draw any triangle which has exactly two lines of symmetry.



(c) Yes, we can draw an equilateral triangle which has three lines of symmetry.

(d) Yes, we can draw a scalene triangle which has no lines of symmetry.

Q.5. On a squared paper, sketch the following :

(a) A triangle with a horizontal line of symmetry but no

vertical line of symmetry.

(b) A quadrilateral with both horizontal and vertical

lines of symmetry.

(c) A quadrilateral with a horizontal line of symmetry

but no vertical line of symmetry.

(d) A hexagon with exactly two lines of symmetry.

(e) A hexagon with six lines of symmetry.



Ans. Sketches of the required figures are shown as under and

dotted lines represents lines of symmetry.

Q.6. Trace each figure and draw the lines of symmetry, if any:



Ans. The line(s) of symmetry of the given figures are shown as under by dotted lines :

Q.7. Consider the letters of English alphabets A to Z. List

among them the letters which have (a) vertical lines of symmetry (like A) (b) horizontal lines of symmetry (like B) (c) no lines of symmetry (like Q)

Ans. The English alphabets A to Z having (a) vertical lines of symmetry : A, H, I, M, O, T, U, V, W,

X, Y. (b) horizontal lines of symmetry : B, C, D, E, H, I, K, O, X.



(c) no lines of symmetry : F, G, J, L, N, P, Q, R, S, Z.

Q.8. Given here are figures of a few folded sheets and designs drawn about the fold. In each case, draw a rough diagram of the complete figure that would be seen when the design is cut off.

Ans. The rough diagram of the complete figure that would be

seen when the design is cut off is as under :

Exercise 13.3

Q.1. Find the number of lines of symmetry in each of the following shapes :

How will you check your answer?



Ans. By drawing the line(s) of symmetry, we find that the

number of line(s) possessed by them are



(a) 4 (b) 1 (c) 2

(d) 2 (e) 1 (f) 2

The object and its image are symmetrical with reference to the mirror line. If the paper is folded, the mirror line becomes the line of symmetry. We will check our answer with the help of mirror line.

Q.2. Copy the following drawing on squared paper. Complete each one of them such that the resulting figure has the two dotted lines as two lines of symmetry :

How did you go about completing the picture?

Ans. The complete figures are given below. Using the given lines of symmetry, we go about completing the picture.



Q.3. In each figure alongside, a letter of the alphabet is shown along with a vertical line. Take the mirror image of the letter in the given line. Find which letters look the same after reflection (i.e., which letters look the same in the image) and which do not. Can you guess why?

Try for O E M N P H L T S V X

Ans. Taking the mirror image of letters A and B in given line. These will look as shown below.

It is clear that after reflection A looks same but B does not

look same. It is due to the reason that the letter A has a vertical line of symmetry where as in B there is no vertical line of symmetry.

Clearly O, M, H, T, V and X look same after reflection, but

E, P, L, and S do not. It is due to the letters E, P, L and S have no vertical line of symmetry.



14 PRACTICAL GEOMETRY

Exercise 14.1

Q.1. Draw a circle of radius 3.2 cm.

Ans. Steps of Construction : (1) Mark a point O on the paper. (2) Open the compasses for the required radius of 3.2 cm. (3) Place the pointer of the compasses on O. (4) Turn the compasses slowly to draw the circle. Be

careful to complete the movement around in one instant.

Q.2. With the same centre O, draw two circles of radii 4 cm

and 2.5 cm.

Ans. Steps of Construction : (1) Mark a point O on the paper. (2) Open the compasses, for the required radius of 4 cm

and 2.5 cm. (3) Place the pointer of the compasses on O.



(4) Turn the compasses slowly to draw the circles with radius 2.5 cm and 4 cm.

(5) These are the required circles.

Note : Circles which have a common centre are called

concentric circles. Q.3. Draw a circle and any two of its diameters. If you join

the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?

Ans. Steps of Construction : (1) Make a point O on the paper and draw a circle with

centre of any radius. (2) Draw any two diameters AB and CD intersecting each

other at O. (3) Join AC, CB, BD and DA.



Here ABCD is a rectangle shown in figure (a)

When the diameters AOB and COD are perpendicular to each other.

Then, on joining AC, CB, BD and DA we get a square

ABCD as shown in figure (b).

Q.4. Draw any circle and mark points A, B and C such that

(a) A is on the circle

(b) B is in the interior of the circle.

(c) C is in the exterior of the circle.

Ans. Steps of Construction :

(1) Draw a circle of any radius with O as centre.



(2) The points are marked as given below (i) Point A on the circle (ii) Point B in the interior of the circle. (iii) Point C in the exterior of the circle.

Q.5. Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether AB and CD are at right angles.

Ans. Steps of construction (1) Mark two points A and B on the paper (2) Taking point A as centre draw a circle of radius AB. (3) Taking point B as centre draw another circle of radius

AB. (4) Circles intersect each other at C and D. Here, on measuring we find ∠CMA = 90º, thus AB and

CD are at right angles so AB ⊥CD.



Exercise 14.2

Q.1. Draw a line segment of length 7.3 cm using a ruler.


(1) Take a point A on the paper and place the ruler so that

zero mark of the ruler is at A (2) With pencil, mark a point B against the mark on the

ruler indicating 7.3 cm. (3) Join the points A and B by moving the tip of the pencil

against the straight edge of the ruler. The line segment AB so obtained is the required line

segment.

Q.2. Construct a line segment of length 5.6 cm using ruler and compasses.


(1) Draw a line l. Mark a point A on a line l. (2) Place the compasses pointer at zero mark on the ruler.

open it to place the pencil point upto the 5.6 cm mark. (3) Put the compasses on line l so that the steel – end is at

A and swing an arc to cut l at B. (4) AB is a line segment of required length.

Q.3. Construct AB of length 7.8 cm. From this, cut off AC of length 4.7 cm. Measure BC.

Ans. Steps of Construction : (1) Draw AB = 7.8 cm



(2) Using compasses, find a point C on AB such that

segment AC = 4.7 cm. (3) On measuring BC, we find that BC = 3.1 cm.

Q.4. Given AB of length 3.9 cm, construct PQ such that the length of PQ is twice that of AB . Verify by measurement.

Construct PX such that length of PX = length of AB; then cut off XQ such that XQ also has the length of AB.


(1) Draw a line l and mark a point P on it.

(2) With the help of compasses find a point X so that PX =

AB = 3.9 cm. on the line l. With the help of compasses find a point Q so that XQ = 3.9 cm. on the line l.

Verification: PQ = PX + XQ = 3.9 cm + 3.9 cm = 2 × 3.9 cm = 2 AB

Q.5. Given AB of length 7.3 cm and CD of length 3.4 cm construct a line segment XY such that the length of XY is equal to the difference between the lengths AB and CD. Verify by measurement.




(1) Draw a line segment AB = 7.3 cm and CD = 3.4 cm.

(2) Draw a line l and take a point X on it. With the help of compasses, find a point P on the line such that XP = AB (i.e., = 7.3 cm). With the help of compasses find a point Y so that the segment PY = segment CD (i.e., 3.4 cm.).

Verification :

XY so obtained is the required line segment, because XY = XP PY AB CD– = –

= 7.3 – 3.4 cm = 3.9 cm.

Exercise 14.3

Q.1. Draw any line segment PQ . Without measuring PQ , construct a copy of PQ .

Ans. Steps of Construction : (1) Given PQ whose length is not known. (2) Fix the compasses pointer on P and the pencil–end on

Q. The opening of the instrument now gives the length of PQ.



(3) Draw any line l. Mark a point A on l. Without changing the compasses setting, place the pointer on A.

(4) Mark an arc that cuts l at a point, say, B. Now AB is a copy of PQ.

Q.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.


(1) Given AB whose length is not known.

(2) Draw any line l. Chose a point O on l. Without changing the compasses setting, place the pointer on O. With the help of pencil end make stroke on the line l to cut it at the point P.

(3) Repeat the process with same opening having P as the O initial point and Q as the terminal points. Thus the segment OQ = OP + PQ = AB + AB = 2AB.

Exercise 14.4

Q.1. Draw any line segment AB. Mark any point M on it. Through M, draw a perpendicular to AB. (use ruler and compasses).




(1) Draw line segment AB, and mark a point M on it. (2) With M as centre and a convenient radius, construct a

part circle (arc) intersecting the line AB at two points C and D.

(3) With C and D as centre and a radius greater than CM, construct two arcs which cut each other at N.

(4) Join MN , now MN is required perpendicular to AB at M, or MN ⊥ AB.

Q.2. Draw any line segment PQ . Take any point R not on it. Through R draw a perpendicular to PQ (use ruler and set-square).


(1) Firstly, draw a line segment PQ and R any point not lying on PQ.

(2) Place the set-square so that the base AB of the set-square lies exactly on the line PQ.

(3) Hold the set-square fixed and place a ruler so that its edge position lies along the side AC of the set-square.



(4) Holding the ruler fixed slide the set-square along the ruler till the point R coincides with the point B of the set-square.

(5) Keeping the set-square fixed in the above position draw a line RT along the edge BC of the set-square through R.

(6) Thus, RT is the required perpendicular line to the line PQ passing through R or, RT ⊥ PQ.

Q.3. Draw a line l and a point X on it. Through X, draw a line segment XY perpendicular to l.

Now draw a perpendicular to XY at Y. (use ruler and compass).


(1) First, draw a line segment l and mark any point X on it.

(2) With centre X and any radius, cut off XA = XB on both sides of X.

(3) With centre A and any radius more than XA draw an

arc, again with centre B and the same radius draw another arc cutting the previously drawn arc at Y.

(4) Join XY, now XY is perpendicular to line l.



(5) By proceeding as above draw a perpendicular YZ to XY.

Exercise 14.5

Q.1. Draw AB of length 7.3 cm and find its axis of symmetry.


(1) Firstly, draw a line segment AB = 7.3 cm.

(2) With A as centre and radius more than 12 AB, draw arcs

one on each side of AB.

(3) With B as centre and the same radius as before, draw arcs cutting the previously drawn arcs at C and D respectively.

(4) Join CD intersecting AB at M, then M bisects the line

segment AB as shown.

Thus, the line segment so obtained is the required axis of symmetry.

Q.2. Draw a line segment of length 9.5 cm and construct its perpendicular bisector.




(1) Draw line segment AB = 9.5 cm.



(3) With B as centre and the same radius as before, draw two arcs intersecting the previously drawn arcs at C and D respectively.

(4) Join CD, then the line segment CD is the required perpendicular bisector of AB.

Q.3. Draw the perpendicular bisector of XY whose length is 10.3 cm.

(a) Take any point P on the bisector drawn. Examine whether PX = PY.

(b) If M is the mid point of XY what can you say about the length MX and XY?


(1) Draw line segment XY = 10.3 cm.



(2) With X as centre and radius more than 12 XY, draw

arcs one on each side of XY.

(3) With Y as centre and the same radius as before, draw two arcs intersecting the previously drawn arcs at A and B respectively.

(4) Join A to B which is intersecting XY at point M, then AB is the required perpendicular bisector of XY.

(a) Mark a point P on the perpendicular bisector AB of XY. On measuring, we find the PX PY= .

(b) M is the mid-point of the segment XY. So that 1MX = XY2 2

1= × 10.3 = 5.15 cm.

Q.4. Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.


(1) Draw line segment AB = 12.8 cm.





(3) With B as centre and the same radius as before, draw two arcs intersecting the previously drawn arcs at C and D respectively.

(4) Join C and D which is intersecting AB at M.

(5) Find the mid-points M1 and M2 of AM and MB respectively proceeding in the same way as before.

Measurement:

AM1 = M1M = MM2 = M2B = 3.3 cm.

Q.5. With PQ of length 6.1 cm as diameter, draw a circle.


(1) Draw PQ = 6.1 cm. on a paper.

(2) Bisect PQ with the help of its perpendicular bisector. Let M be its mid-point.

(3) Draw a circle with M as centre and radius MP.

(4) The circle so obtained is the required circle.

Q.6. Draw a circle with centre C and radius 3.4 cm. Draw any chord AB . Construct the perpendicular bisector of AB and examine if it passes through C.




(1) Mark a point C on a paper.

(2) With C as centre and radius 3.4 cm draw a circle.

(3) Let, AB be any chord of this circle.

(4) Draw the perpendicular bisector PQ of chord AB. Here, this perpendicular bisector passes through C which is, the centre of the circle.

Q.7. Repeat Question 6, if AB happens to be a diameter.

Ans. If AB happens to be a diameter then C will be the mid point of the diameter AB or C will be centre of the circle.

Q.8. Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?


(1) Mark a point O on the paper.

(2) With O as centre, draw a circle of radius 4 cm.



(3) Let AB and CD be any two chords of this circle.

(4) Draw the perpendicular bisector PQ and RS of chords AB and CD respectively.

Here, these perpendicular bisector pass through O which is the centre of circle.

Q.9. Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of OA and OB. Let them meet at P. Is PA = PB?


(1) Draw ∠XOY of any measure.

(2) Take a point A on OX and a point B on OY such that OA = OB.

(3) Draw the perpendicular bisectors CD and EF of OA and OB respectively. Let them meet at P.

(4) Join PA and PB. On measuring, PA = PB.



Exercise 14.6

Q.1. Draw ∠POQ of measure 75º and find its line of symmetry?


(1) Draw OQ of any length.

(2) Place the centre of the protractor at O and the zero edge along OQ.

(3) Count with zero near Q. Mark point P at 75º.

(4) Join OP , then ∠POQ = 75º which is required angle.

(5) With O as centre and with the help of compasses, draw an arc that cuts both rays of ∠POQ. Mark the points of intersection as A and B.

(6) With B as centre, draw (in the interior of ∠POQ) an arc where radius is more than half the length AB.

(7) With the same radius and with A as centre, draw another arc in the interior of ∠POQ. Let the two arcs intersect at R. Then, OR is the bisector of ∠POQ. Which is also the line of symmetry of ∠POQ as ∠POR = ∠ROQ.

Q.2. Draw an angle of measure 147º and construct its bisector.




(1) Draw a ray OA.

(2) Place the centre of protractor at O so that 0 – 180º line lies along OA.

(3) Start with 180º mark a point B on the paper against the mark of 147º on the protractor.

(4) Replace the protractor and draw OB. Then, the ∠AOB so obtained is the required angle such that ∠AOB = 147º.

Steps of Construction of the bisector of 147º:

(1) With O as centre and a convenient radius draw an arc intersecting sides OA and OB at P and Q respectively.

(2) With P as centre and radius more than 12 PQ, draw an

arc.

(3) With Q as centre and the same radius, as in the previous step, draw another arc intersecting at R to the arc drawn in the previous step.

(4) Join OR and produce it such that it form a ray OC.

Then, the ∠AOC so obtained is the required bisector of ∠AOB.



Q.3. Draw a right angle and construct its bisector?


(1) Draw a ray OA.

(2) With O as centre and any convenient radius, draw an arc intersecting OA at P.

(3) With P as centre and same radius, draw an arc intersecting the arc of step 2 at Q.

(4) With Q as centre the same radius as in steps 2 and 3 draw an arc intersecting the arc drawn in step 3 at R.

(5) With Q as centre and the same radius, drawn an arc.

(6) With R as centre and the same radius, drawn an arc intersecting the arc drawn in step 5 at B.

(7) Joint OB and join it to C, then ∠AOC is a right angle.

Steps of Construction of the bisector of 90º :

(1) With P as centre and radius more than 12 PT, draw an

arc in the interior of ∠AOC.

(2) With T as centre and the same radius as is step 1, draw another arc intersecting the arc in step 1 at D.

(3) Join OD and produce it to E, then ∠AOE so obtained is the required bisector of ∠AOC.



Q.4. Draw an angle of measure 153º and divide it into four equal parts.


(1) Draw ∠AOB = 153º with the help of the protractor.

(2) With O as centre and any convenient radius, draw an arc intersecting OA and OB at P and Q respectively.

(3) With P as centre and radius more than 12 PQ draw an

arc in the interior of ∠AOB.

(4) With Q as centre and the same radius, as in step 3, draw another arc intersecting the arc in step 3 at B1.

(5) Join OB1, and produce it to C.

Then, ∠AOC = 12 × ∠AOB i.e., OC is the bisector of

∠AOB.

(6) Similarly, draw OD, the bisector of ∠AOC. Then, ∠AOD = ∠DOC.

(7) Similarly, draw OE, the bisector of ∠COB. Then, ∠COE = ∠EOB.

Taking the above results we find.

∠AOD = ∠DOC = ∠COE = ∠EOB



Thus, ∠AOB is divided into four equal parts by the rays OD, OC and OE

Q.5. Construct with ruler and compasses, angles of following measures :

(a) 60º (b) 30º (c) 90º (d) 120º (e) 45º (f) 135°

Ans. Steps of Construction of measure 60º :

(a) (1) Draw a ray OA.

(2) With O as centre and any radius, draw arc PQ with the help of compasses, intersecting the ray OA at P.

(3) With P as centre and the same radius draw an arc intersecting the arc PQ at R.

(4) Join OR and Produce it to obtain ray OB.

Then, ∠AOB = 60º.

(b) Steps of construction of measure 30º. (1) Draw a ray OA. (2) With O as centre any radius, draw an arc PQ with

the help of compasses, intersecting ray OA at P.

(3) With P as centre and the same radius draw an arc intersecting the arc PQ at R.

(4) Join OR and produce it to obtain ray OB. Then, ∠AOB = 60º.



(5) With P as centre and radius more than 12 PR, draw

an arc in the interior of ∠AOB.

(6) With R as centre and the same radius, as in step 5, draw another arc intersecting the arc in step 5 at M.

(7) Join OM and produce it to any point C.

Thus, ∠AOC = 30º.

(c) Steps of construction of measure 90º.

(1) Draw a ray OA.

(2) With O as centre and any convenient radius draw an arc intersecting the ray OA at P.

(3) With P as centre and same radius, draw an arc intersecting the arc of step 2 at Q.

(4) With Q as centre and the same radius as in steps 2 and 3, draw an arc intersecting the arc drawn in step 3 at R.


(6) With R as centre and the same radius, draw an arc drawn in step 5 at B.

(7) Join O to B and join it to any point C then, ∠AOC = 90º.

(d) Steps of construction of measure 120º.

(1) Draw a ray OA.

(2) With O as centre and any convenient radius draw an arc intersecting OA at P.



(3) With P as centre and the same radius draw an arc intersecting the first arc at Q.

(4) With Q as centre and the same radius draw an arc intersecting the arc drawn in step 2 at R.

(5) Join OR and produce it to any point C. Then,

∠AOC so obtained is of 120º.

(e) Steps of construction of measure 45º. (1) Draw a ray OA. (2) With O as centre and any convenient radius draw

an arc intersecting the ray OA at P. (3) With P as centre and same radius, draw an arc

intersecting the arc of step 2 at Q. (4) With Q as centre and the same radius as in steps 2

and 3, draw an arc intersecting the arc drawn in step 3 at R.


(6) With R as centre and the same radius, draw an arc drawn in step 5 at B.

(7) Join O to B and join it to any point C then, ∠AOC = 90º.



(8) With P as centre and radius more than 12

PT,

draw on arc in the interior of AOB.

(9) With T as centre and the same radius, as in step 8, draw another arc intersencting the arc in step at D.

(10) Join OD and produce it to any point E. Thus, ∠AOE = 45°.

(f) Steps of construction of measure 135º.

(1) Draw a line AB take a point O on it.

(2) With O as centre and any convenient radius draw

a semi-circle intersecting OA and OB at P and Q respectively.

(3) With Q as centre and same radius draw an arc intersecting the semi-circle at R

(4) With R as centre and same radius, draw an arc cutting the semi-circle of step 2 at S.

(5) With R as centre and same radius draw an arc.



(6) With S as centre and same radius draw an arc intersecting the arc drawn in step 5 at T. Join OT and produce it to D such that ∠BOD = ∠AOD = 90º.

(7) Draw the bisector OE of ∠AOD.

Then,

∠BOE = ∠BOD + ∠DOE

= 90º + 12 × ∠AOD

= 90º + 12 × 90º

= 90º + 45º

= 135º, which is the required angle.

Q.6. Draw an angle of measure 45º and bisect it.


(1) Draw ∠AOB = 90º by the steps given in question 5(c).

(2) Draw the bisector OC of ∠AOB, then ∠AOC = 45º.

(3) With P and Q as centres draw two arcs intersecting at S. Join OS and produce it to D.



(4) ∠AOD = ∠DOC or ∠AOD = 12 ∠AOC = 1

2 × 45º.

Thus, OD is the required bisector of ∠AOC.

Q.7. Draw an angle of measure 135º and bisect it.


(1) Draw ∠EOB = 135º using the steps given in question 5 (f).

(2) With Q and N as centers, draw two respective arcs intersecting at a point M. Draw the ray OF passing through M.

(3) OF is the required bisector of ∠EOB = 135º, where ∠BOF = ∠EOF.

Q.8. Draw an angle of 70º. Make a copy of it using only a straight edge and compasses.


(1) Draw OQ of any length. (2) Place the centre of protractor at O and zero edge along

OQ. (3) Count 0 near Q. Mark point P at 70°.

(4) Join, OP then ∠POQ = 70° which is required angle.



To Construct the copy of ∠POQ (1) Draw O′Q′ of any length with the help of straight ruler. (2) With O as centre and with the help of compasses draw

an arc that cuts both rays of ∠POQ. Mark the points of intersection as A and B

(3) With the same radius as in step 2 draw an arc AB with O′ as centre on O′Q′.

(4) With A as centre draw an arc to interest OP at C. (5) With the same radius as in step (4) draw an arc with

centre A′ to intersect O′P′ at C′. (6) Join O′C′ and produce it to P′. (7) ∠P′O′Q′ is the required copy of angle 70°.

Q.9. Draw an angle of 40º. Copy its supplementary angle. Ans. Steps to construct angle of 40° (1) Draw AB of any length. (2) Place the centre of protractor at A so that 0 – 180° line

lies along AB.

(3) Mark a point C on the paper against the mark of 40°.



(4) Reduce protractor and draw AC. (5) ∠BAC = 40° is the required angle. Steps to construct supplementary angle of 40°

(1) Produce AD in the opposite direction of to draw ∠DAC which is supplementary angle of ∠BAC.

AD

(2) Following the procedure as given in Q. 8 we can draw ∠D′A′C′.

(3) ∠D′A′C′ is the required copy of supplementary angle

40°.

exercise 13 - testlabz · diagram to make it symmetric. ans. the complete diagram is as under :...

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