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ML Aggarwal Class 6 Solutions Chapter 13 Practical Geometry Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A ruler is used to draw a line and to measure their …………
(ii) A divider is used to compare …………
(iii) A compass is used to draw circles or arcs of …………
(iv) A protractor is used to draw and measure …………
(v) The set squares are two triangular pieces having angles of ………… and …………
(vi) To bisect a line segment of length 7 cm, the opening of the’ compass should be more than …………
(vii) The perpendicular bisector of a line segment is also its line of …………
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) There is only one set square in a geometry box.
(ii) An angle can be copied with the help of a ruler and compass.
(iii) The perpendicular bisector of a line segment can be drawn by paper folding.
(iv) Perpendicular to a line from a given point not on it can be drawn by paper folding.
(v) A 45° – 45° – 90° set square and a protractor have the same number of line(s) of symmetry.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 13):
Question 3.
A circle of any radius can be constructed with the help of a:
(a) ruler
(b) divider
(c) compass
(d) protractor
Solution:
compass (c)

Question 4.
The instrument in a geometry box having the shape of a semicircle is :
(a) ruler
(b) divider
(c) compass
(d) protractor
Solution:

Question 5.
The instrument to measure an angle is
(a) ruler
(b) protractor.
(c) divider
(d) compass
Solution:
protractor (b)

Question 6.
Which of the following angles cannot be constructed using a ruler and compass?
(a) 15°
(b) 45°
(c) 75°
(d) 85°
Solution:
85° (d)

Question 7.
The number of perpendiculars that can be drawn to a line from a point not on it is
(a) 1
(b) 2
(c) 4
(d) infinitely many
Solution:
1 (a)

Question 8.
The number of perpendicular bisectors that can be drawn of a given line segment is :
(a) 0
(b) 1
(c) 2
(d) infinitely many
Solution:
1 (b)

Question 9.
The number of lines of symmetry in a picture of a divider is The number of lines of symmetry in a picture of a compass is
(a) 0
(b) 1
(c) 2
(d) 4
Solution:
1 (b)

Question 10.
The number of lines of symmetry in a picture of a compass is
(a) 0
(b) 1
(c) 2
(d) none of these
Solution:
0 (a)

Question 11.
The number of lines of symmetry in a ruler is
(a) 0
(b) 1
(c) 2
(d) 4
Solution:
2 (c)

Question 12.
The number of lines of symmetry in a 30° – 60° – 90° set square is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:
0 (a)

Question 13.
The number of lines of symmetry in a protractor is
(a) 0
(b) 1
(c) 2
(d) more than 2
Solution:
1 (b)

ML Aggarwal Class 6 Solutions Chapter 13 Practical Geometry Ex 13.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.3

Question 1.
Draw an angle of 80° and make a copy of it using ruler and compass.
Solution:

Question 2.
Draw an angle of measure 127° and construct its bisector.
Solution:

Question 3.
Draw ∠POQ = 64°. Also, draw its line of symmetry.
Solution:

Question 4.
Draw a right angle and construct its bisector.
Solution:

Question 5.
Draw an angle of 152° and divide it into four equal parts.
Solution:

Question 6.
Draw an angle of measure 45° and bisect it.
Solution:

ML Aggarwal Class 6 Solutions Chapter 13 Practical Geometry Ex 13.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.2

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

Question 2.
Draw a line segment \(\overline{\mathrm{AB}}\) = 6.2 cm. Draw a perpendicular to it at a point M on \(\overline{\mathrm{AB}}\) by using ruler and compass.
Solution:

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

Question 4.
Draw a line segment \(\overline{\mathrm{AB}}\) of length 6.4 cm and construct its axis of symmetry (use ruler and compass).
Solution:

Question 5.
Draw the perpendicular bisector of \(\overline{\mathrm{XY}}\) 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 \(\overline{\mathrm{XY}}\), what can you say about the lengths MX and MY?
Solution:

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.
Solution:

Question 7.
With \(\overline{\mathrm{PQ}}\) of length 5.6 cm as diameter, draw a circle.
Solution:

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.
Solution:

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?
Solution:

ML Aggarwal Class 6 Solutions Chapter 13 Practical Geometry Ex 13.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13.1

Question 1.
Construct a circle of radius:
(i) 2 cm
(ii) 3.5 cm
Solution:

Question 2.
With the same centre O, draw two circles of radii 2.6 cm and 4.1 cm.
Solution:

Question 3.
Draw any circle and mark points A, B and C such that
(i) A is on the circle.
(ii) B is in the interior of the circle.
(iii) C is in the exterior of the circle.
Solution:

Question 4.
Draw a circle and any two of its (non-perpendicular) 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?
Solution:

Question 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 \(\overline{\mathrm{AB}}\) and \(\overline{\mathrm{CD}}\) are at right angles.
Solution:

Question 6.
Construct a line segment of the length of 6.3 cm using ruler and compass.
Solution:

Question 7.
Construct \(\overline{\mathrm{AB}}\) of length 8.3 cm. From this cut off \(\overline{\mathrm{AC}}\) of length 5.6 cm. Measure the length of BC . .
Solution:

Question 8.
Draw any line segment \(\overline{\mathrm{PQ}}\). Without measure \(\overline{\mathrm{PQ}}\), construct a copy of \(\overline{\mathrm{PQ}}\).
Solution:

Question 9.
Given some line segment \(\overline{\mathrm{AB}}\), whose length you do not know, construct \(\overline{\mathrm{PQ}}\) such that the length of \(\overline{\mathrm{PQ}}\) is twice that of \(\overline{\mathrm{AB}}\).
Solution:

Question 10.
Take a line segment \(\overline{\mathrm{PQ}}\) of length 10 cm. From \(\overline{\mathrm{PQ}}\), cut of \(\overline{\mathrm{PA}}\) of length 4.3 cm and \(\overline{\mathrm{BQ}}\) of length 2.5 cm. Measure the length of segment \(\overline{\mathrm{AB}}\).
Solution:

Question 11.
Given two line segments \(\overline{\mathrm{AB}}\) and \(\overline{\mathrm{CD}}\) of length 7.5 cm and 4.6 respectively. Construct line segments.
(i) \(\overrightarrow { PQ } \) of length equal to the sum of the lengths of \(\overline{\mathrm{AB}}\) and \(\overline{\mathrm{CD}}\).
(ii) \(\overline{\mathrm{XY}}\) of length equal to the difference of the lengths of \(\overline{\mathrm{AB}}\) and \(\overline{\mathrm{CD}}\). Verify these lengths by measurements.
Solution:

ML Aggarwal Class 6 Solutions Chapter 12 Symmetry Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 12 Symmetry Check Your Progress

Question 1.
Draw the line (or lines) of symmetry, if any, of the following figures/shapes and count their number:

Solution:

Question 2.
Draw the line (or lines) of symmetry, if any, of the following pictures of playing cards and count their number:

Solution:

Question 3.
Write the letters of the word ‘ALGEBRA’ which have no line of symmetry.
Solution:
L, G, R

Question 4.
On a squared paper, sketch the following:
(i) A triangle with a horizontal line of symmetry but no vertical line of symmetry.
(ii) A quadrilateral with both horizontal and vertical lines of symmetry.
(iii) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.
(iv) A hexagon with exactly two lines of symmetry.
Solution:

Question 5.
Copy the following figures on a squared paper and complete each figure such that the resultant figure is symmetrical about the dotted line (or lines):

Solution:

Question 6.
State whether the following statement is true or false. Justify your answer:
“A straight line dividing a figure into two identical parts is necessarily a line of symmetry.”
Solution:

Question 7.
Find whether the figure on the left side is the reflection of the figure on right side. If not, draw the correct figure.

Solution: