ML Aggarwal Practical Geometry Exe-13.2 Class 6 ICSE Maths Solutions

ML Aggarwal Practical Geometry Exe-13.2 Class 6 ICSE Maths Solutions. We Provide Step by Step Answer of  Exe-13.2 Questions for Practical Geometry as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-6.

ML Aggarwal Practical Geometry Exe-13.2 Class 6 ICSE Maths Solutions

Board ICSE
Publications Avichal Publishig Company (APC)
Subject Maths
Class 6th
Chapter-13 Practical Geometry
Writer ML Aggarwal
Book Name Understanding
Topics Solution of Exe-13.2 Questions
Edition 2023-2024

Practical Geometry Exe-13.2

ML Aggarwal Class 6 ICSE Maths Solutions

Page-277

Question 1. Draw a line segment PQ =5.6 cm. Draw a perpendicular to it from a point A outside \overline{\mathrm{PQ}} by using ruler and compass.

Answer:

Given: A-Line segment PQ = 5.6 cm and a point A outside the line.
Required: To draw a 1 ar to PQ from point A.

Steps of construction :

(i) With A as centre and any suitable radius,
drawn an arc to cut the line PQ at points C and D.
(ii) With C and D as centres, drawn two arcs of equal radius ( > 1/2 CD)
cutting each other at B on the other side of PQ.
(iii) Join A and B to meet the line PQ at N,
then AN is the required perpendicular from the point A to the line PQ.

Question 1. Draw a line segment PQ =5.6 cm. Draw a perpendicular to it from a point A outside  by using ruler and compass.

Question 2. Draw a line segment AB = 6.2 cm. Draw a perpendicular to it at a point M on AB by using ruler and compass.

Answer:

Given: A line AB = 6.2 cm and a point P on it.
Required: To draw an ⊥ arc to AB at point P.

Question 2. Draw a line segment AB = 6.2 cm. Draw a perpendicular to it at a point M on AB by using ruler and compass.

Step of Construction :

(i) With P as centre and any suitable radius,
draw an arc to cut the line AB at points C and D.
(ii) With C and D as centres,
draw two arcs of equal radius ( > 1/2 CD)  cutting each other at Q.
(iii) Join P and Q.
then QP is the required perpendicular to the line AB at the point P.


Practical Geometry Exe-13.2

ML Aggarwal Class 6 ICSE Maths Solutions

Page-278

Question 3. Draw a line l and take a point P on it. Through P, draw a line segment PQ perpendicular to l. Now draw a perpendicular to PQ at Q (use ruler and compass).

Answer:

Steps of construction :

(i) Let AB be the given line segment.
(ii) With A as centre and any suitable radius ( > 1/2 CD)
draw arcs on each side of AB.
(iii) With B as centre and same radius [as in step (i)],
draw arcs on each side of AB to cut the previous arcs at P and Q.
(iv) Draw a line passing through points P and Q,
then the lines PQ is the required perpendicular bisector of AB and line l.

Question 3. Draw a line l and take a point P on it. Through P, draw a line segment PQ perpendicular to l. Now draw a perpendicular to PQ at Q (use ruler and compass).

Question 4. Draw a line segment AB of length 6.4 cm and construct its axis of symmetry (use ruler and compass).

Answer:

Steps of construction :

(i) Draw a line segment AB  of length 6.4 cm.
(ii) With A as centre, using a compass, draw a circle.
The radius of this circle should be more than half of the length of AB.
(iii) With the same radius and with B as centre,
draw another circle using a compass.
Let it cut the previous circle at C and D.
(iv) Join CD. Then, CD is the axis of symmetry of AB .

Question 4. Draw a line segment AB of length 6.4 cm and construct its axis of symmetry (use ruler and compass).

Question 5. Draw the perpendicular bisector of XY whose length is 8.3 cm.

(i) Take any point P on the bisector drawn. Examine whether PX = PY.
(ii) If M is the mid-point of XY , what can you say about the lengths MX and MY?

Answer:

Steps of construction :

(i) Draw a line segment XY  of length 8.3 cm.
(ii) With X as centre, using compass, draw a circle.
The radius of this circle should be more than half of the length of XY .
(iii) With the same radius and with Y as centre,
draw another circle using a compass.
Let it cut the previous circle at A and B.
(iv) Join AB.
Then, AB is the perpendicular bisector of the line segment XY .

Question 5. Draw the perpendicular bisector of XY whose length is 8.3 cm.

(a) On examination, we find the PX = PY.
(b) We can say that the length of MX is Equal to the length of MY.

Question 6. Draw a line segment of length 8.8 cm. Using ruler and compass, divide it into four equal parts. Verify by actual measurement.

Answer:

Steps of construction :

(i) Draw a line segment AB of length 8.8 cm.
(ii) With A as centre, using compass,
draw two arcs on either side of AB.
The radius of this arc should be more than half of the length of \overline{\mathrm{AB}}.
(iii) With the same radius and with B as ctntre,
draw another arc using compass.
Let it cut the previous arc at C and D.
(iv) Join CD.
It cuts AB at E.
Then CD is the perpendicular bisector of the line segment AB.
(v) With A as centre, using compass, draw a circle.
The radius of this circle should be more than half of the length of Ac.
(vi) With the same radius and with E as ceitre,
draw another circle using compass.
Let it cut the previous circle at F ana G.
(vii) Join FG . It cuts AE at H.
Then FG is the perpendicular bisector of the line segment AE.
(viii) With E as centre, using compass, draw a circle.
The radius of the circle should be more than half of the length of EB.
(ix) With the same radius md with B is centre,
draw another circle using compass.
Let it cut the previous cirde at I and J.

Question 6. Draw a line segment of length 8.8 cm. Using ruler and compass, divide it into four equal parts. Verify by actual measurement.

(x) Join IJ . It cuts EB at K.
Then IJ is the perpendicular bisector of the line segment EB.
Now, the points H, E and K divide AB into four equal parts. i. e.,
AH = HE = EK = KB
By measurement,
AH = HE = EK = KB = 2.2 cm

Question 7. With PQ of length 5.6 cm as diameter, draw a circle.

Answer:

Steps of construction :

(i) Draw a line segment PQ of length 5.6 cm.
(ii) With P as centre, using compass, draw a circle.
The radius of this circle should be more than half of the length of PQ.
(iii) With the same radius and with Q as centre,
draw another circle using compass.
Let it cut the previous circle at A and B.
(iv) Join AB. It cuts PQ at C.
Then AB is the perpendicular bisector of the line segment PQ.
(v) Place the pointer of the compass at C
and open the pencil up to P.
(vi) Turn the compass slowly to draw the circle.

Question 7. With PQ of length 5.6 cm as diameter, draw a circle.

Question 8. Draw a circle with centre C and radius 4.2 cm. Draw any chord AB. Construct the perpendicular bisector of AB and examine if it passes through C.

Answer:

Steps of construction :

(i) Draw a point with a sharp pencil aid mark it as C.
(ii) Open the compass for the required radius of 4.2 cm,
by putting the pointer on 0 and opening the pencil up to 4.2 cm.
(iii) Place the pointer of the compass at C.
(iv) Turn the compass slowly to draw the circle.
(v) Draw any chord AB of this circle.
(vi) With A as centre, using compass, draw a circle.
The radius of this circle should be more than half of the length of AB.
(vii) With the same radius and with B as centre,
draw another circle using compass.
Let it cut the previous circle at D and E.
(viii) Join DE.
Then DE is the perpendicular bisector of the line segment AB.
On examination, we find that it passes through C.

Question 8. Draw a circle with centre C and radius 4.2 cm. Draw any chord AB. Construct the perpendicular bisector of AB and examine if it passes through C.

Question 9. Draw a circle of radius 3.5 cm. Draw any two of its (non-parallel) chords. Construct the perpendicular bisectors of these chords. Where do they meet?

Answer:

Steps of construction :

(i) Draw a point with a sharp pencil and mark it as O.
(ii) Open the compasses for the required radius 3.5 cm,
by putting the pointer on 0 and opening the pencil upto 3.5 cm.
(iii) Place the pointer of the compass at O.
(iv) Turn the compass slowly to draw the circle.
(v) Draw any two chords AB and CD of this circle.
(vi) With A as centre, using compass, draw two arcs on either side of AB.
The radius of this arc should be more than half of the length of AB.
(vii) With the same radius and with B as centre,
draw another two arcs using compass.
Let it cut the previous circle at E and F.
(viii) Join EF.
Then EF is the perpendicular bisector of the chord AB.
(ix) With C as centre, using compass,
draw two arcs on either side of CD.
The radius of this arc should be more than half of the length of CD.
(x) With the same radius and with D as centre,
draw another two arcs using a compass.
Let it cut the previous circle at G and H.
(xi) Join GH.
Then GH is the perpendicular bisector of the chord CD.
We find that perpendicular bisectors EF and GH meet at O,
the centre of the circle.

Question 9. Draw a circle of radius 3.5 cm. Draw any two of its (non-parallel) chords. Construct the perpendicular bisectors of these chords. Where do they meet?

—  : End of ML Aggarwal Practical Geometry Exe-13.2 Class 6 ICSE Maths Solutions :–

Return to   ML Aggarwal Maths Solutions for ICSE Class -6

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