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ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes Ex 11.2 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 11 Understanding Symmetrical Shapes Ex 11.2

Question 1.
What fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from:
(i) 4 to 10
(ii) 2 to 5
(iii) 7 to 10
(iv) 8 to 5
(v) 11 to 5
(vi) 6 to 3
Also find the number of right angles turned in each case.
Solution:

Question 2.
Where will the hand of a clock stop if it
(i) starts at 10 and makes \(\frac{1}{2}\) of a revolution, clockwise?
(ii) starts at 4 and makes \(\frac{1}{4}\) of a revolution, clockwise?
(iii) starts at 4 and makes \(\frac{3}{4}\) of a revolution, clockwise?
Solution:

Question 3.
Where will the hand of a clock stop if it starts from
(i) 6 and turns through 1 right angle?
(ii) 8 and turns through 2 right angles?
(iii) 10 and turns through 3 right angles?
(iv) 7 and turns through 2 straight angles?
Solution:

Question 4.
What fraction of a revolution have you turned through if you stand facing
(i) north and turn clockwise to face west?
(ii)south and turn anti-clockwise to face east?
(iii) east and turn clockwise (or anti-clockwise) to face west?
Also find the number of right angles turned in each case.
Solution:

Question 5.
Match the following

Solution:

Question 6.
Classify the angles whose magnitudes are given below:
(i) 56°
(ii) 125°
(iii) 90°
(iv) 180°
(v) 215°
(vi) 328°
(vii) 89°
(viii) 178°
Solution:

Question 7.
State which of the following angles with a small letter in the following diagrams are acute, which obtuse and which are reflex:


Solution:

Question 8.
Use your protector to measure each of the angles marked in the following figures:

Solution:

Question 9.
Use your protector to measure the reflex angles marked in the following figures:

Solution:

Question 10.
Find the measure of the angle between the hands of the clock in each figure:

Solution:

Question 11.
Write the measure of the smaller angle formed by the hour and the minutes hands of a clock at 7 O’clock. Also write the measure of the other angle and also state what types of angles these are.
Solution:

Question 12.
There are two set-squares in your geometry box. What are measures of the angles formed at their corners? Do they have any angle measure that is common?
Solution:

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes Ex 11.1 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 11 Understanding Symmetrical Shapes Ex 11.1

Question 1.
Why is it better to use a divider and a ruler than a ruler only, while measuring the length of a line segment?
Solution:

Question 2.
In the given figure, compare the line segments with the help of a divider and fill in the blanks by using the symbol >, = or <:
(i) AB ………. CD
(ii) BC ………. AB
(iii) AC ………. BD
(iv) CD ………. BD

Solution:

Question 3.
If A, B and C are collinear points such that AB = 6 cm, BC = 4 cm and AC = 10 cm, which one of them lies between the other two?
Solution:

Question 4.
In the given figure, verify the following by measurement:
(i) AB + BC = AC
(ii) AC – BC = AB

Solution:

Question 5.
In the given figure, verify by measurement that:
(i) AC + BD = AD + BC
(ii) AB + CD = AD – BC

Solution:

Question 6.
In the given figure, measure the lengths of the sides of the triangle ABC and verify:
(i) AB + BC > AC
(ii) BC + AC > AB
(iii) AC + AB > BC

Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept 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 10 Basic Geometrical Concept Check Your Progress

Question 1.
(i) Name all the rays shown in the given figure whose initial point is A.
(ii) Is ray \(\overrightarrow{\mathrm{AB}}\) different from ray \(\overrightarrow{\mathrm{AD}}\) ?
(iii) Is ray \(\overrightarrow{\mathrm{CA}}\) different from ray \(\overrightarrow{\mathrm{CE}}\) ?
(iv) Is ray \(\overrightarrow{\mathrm{BA}}\) different from ray \(\overrightarrow{\mathrm{CA}}\) ?
(v) Is ray \(\overrightarrow{\mathrm{ED}}\) different from ray \(\overrightarrow{\mathrm{DE}}\) ?

Solution:

Question 2.
From the given figure, write

(i) all pairs of parallel lines.
(ii) all pairs of intersecting lines.
(iii) lines whose point of intersecting is E.
(iv) collinear points.
Solution:

Question 3.
In the given figure :

(a) Name;
(i) Parallel lines.
(ii) All pairs of intersecting lines.
(iii) concurrent lines.
(b) State wheather true or false:
(i) points A, B and D are collinear.
(ii) lines AB and ED interesect at C.
Solution:

Question 4.
In context of the given figure, state whether the following statements are true (T) or false (F):

(i) Point A is in the interior of ∠AOD.
(ii) Point B is in the interior of ∠AOC.
(iii) Point C is in the exterior of ∠AOB.
(iv) Point D is in the exterior of ∠AOC.
Solution:

Question 5.
How many angles are marked in the given figure? Name them?

Solution:

Question 6.
In context of the given figure, name
(i) all triangles
(ii) all triangles having point E as common vertex.

Solution:

Question 7.
In context of the given figure, answer the following questions:

(i) Is ABCDEFG a polygon?
(ii) How many sides does it have?
(iii) How many vertices does it have?
(iv) Are \(\overline{\mathrm{AB}}\)
and \(\overline{\mathrm{FE}}\) adjacent sides?
(v) Is \(\overline{\mathrm{GF}}\)
a diagonal of the polygon?
(vi) Are \(\overline{\mathrm{AC}}, \overline{\mathrm{AD}} \text { and } \overline{\mathrm{AE}}\) diagonals of the polygon?
(vii) Is point P in the interior of the polygon?
(viii)Is point A in the exterior of the polygon?
Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept 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 10 Basic Geometrical Concept Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) There is exactly one line passing through ……….. distinct points in a plane.
(ii) Two different lines in a plane either ……….. at exactly one point or are parallel.
(iii) The curves which have different beginning and end points are called ……….. curves.
(iv) A curve which does not cross itself at any point is called a ……….. curve.
(v) A simple closed curve made up entirely of line segments is called a ………..
(vi) A line segment formed by joining two non- adjacent vertices of a polygon is called its ………..
(vii) A quadrilateral has ……….. diagonals.
(viii) A lines segment has a ……….. length.
Solution:

Question 2.
Fill in the blanks with correct word(s) to make the statement true.
(i) Radius of a circle is one-half of its ………..
(ii) A radius of a circle is a line segment with one end point
at ……….. and the other end-point on
(iii) A chord of a circle is a line segment with its end points ………..
(iv) A diameter of a circle is a chord that ……….. the centre of the circle.
(v) All radii of a circle are ………..
Solution:

Question 3.
State whether the following statements are true (T) or false (F):
(i) The line segment AB is the shortest route from A to B.
(ii) A line cannot be drawn wholly on a sheet of paper..
(iii) A line segment is made of infinite (uncountable) number of points.
(iv) Two lines in a plane always intersect.
(v) Through a given point only one line can be drawn.
(vi) Two different lines can be drawn passing through two distinct points.
(vii) Every simple closed curve is a polygon.
(viii)Every polygon has atleast three sides.
(ix) A vertex of a quadrilateral lies in its interior.
(x) A line segment with its end-points lying on a circle is called a diameter of the circle.
(xi) Diameter is the longest chord of the circle.
(xii) The end-points of a diameter of a circle divide the circle into two points, each part is called a semi-circle.
(xiii) A diameter of a circle divides the circular region into two parts, each part is called a semi-circular region.
(xiv) The diameter’s of a circle are concurrent the centre of the circle is the point common to all diameters.
(xv) Every circle has unique centre and it lies inside the circle.
(xvi) Every circle has unique diameter.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (4 to 20):
Question 4.
Which of the following has no end points?
(a) a line
(b) a ray
(c) a line segment
(d) none of these
Solution:

Question 5.
Which of the following has definite length?
(a) a line
(b) a ray
(c) a line segment
(d) none of these
Solution:

Question 6.
The number of points required to name a line if
(a) 1
(b) 2
(c) 3
(d) 4
Solution:

Question 7.
The number of lines that can be drawn through a given point is
(a) 1
(b) 2
(c) 3
(d) infinitely many
Solution:

Question 8.
The number of lines that can be drawn passing through two distinct points is
(a) 1
(b) 2
(c) 3
(d) inifinitely many
Solution:

Question 9.
The maximum number of points of intersection of three lines drawn in a plane is
(a) 1
(b) 2
(c) 3
(d) 6
Solution:

Question 10.
The minimum number of points of intersection of three lines drawn in a plane is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:

Question 11.
In the given figure, the number of line segment is
(a) 5
(b) 10
(c) 12
(d) 15
Solution:

Question 12.
In a polygon with 5 sides, the number of diagonals is
(a) 3
(b) 4
(c) 5
(d) 10
Solution:

Question 13.
The number of lines passing through 5 points such that no three of them are collinear are
(a) 10
(b) 5
(c) 8
(d) 20
Solution:

Question 14.
In context of the given figure, which of the following statement is correct ?
(a) B is not a point on segment \(\overline{\mathrm{AC}}\)
(b) B is the initial point of the ray \(\overrightarrow{\mathrm{AD}}\)
(c) D is a point on the ray \(\overrightarrow{\mathrm{CA}}\)
(d) C is a point on the ray \(\overrightarrow{\mathrm{BD}}\)

Solution:

Question 15.
The figure formed by two rays with same initial point is known as
(a) a line
(b) a line segment
(c) a ray
(d) an angle
Solution:

Question 16.
In the given figure, the number of angles is
(a) 3
(b) 4
(c) 5
(d) 6

Solution:

Question 17.
Which of the following statements is false?
(a) A triangle has three sides
(b) A triangle has three vertices
(c) A triangle has three angles
(d) A triangle has two diagonals
Solution:

Question 18.
Which of the following statements is false?
(a) A quadrilateral has four sides and four vertices
(b) A quadrilateral has four angles
(c) A quadrilateral has four diagonals
(d) A quadrilateral has two diagonals
Solution:

Question 19.
By joining any two points of a circle, we obtain its
(a) radius
(b) chord
(c) diameter
(d) circumference
Solution:

Question 20.
If the radius of a circle is 4 cm, then the length of its diameter is
(a) 2 cm
(b) 4 cm
(c) 8 cm
(d) 16 cm
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
Can a sector and segment of a circle coincide? If so, name it.
Solution:

Question 2.
In the given figure, find:
(i) the number of triangles pointing up.
(ii) the total number of triangles.

Solution:

Question 3.
In the given figure, find the total number of squares.

Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Ex 10.4 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 10 Basic Geometrical Concept Ex 10.4

Question 1.
In the given figure, identify:
(i) the centre of the circle
(ii) three radii
(iii) a diameter
(iv) a chord
(v) two points in the interior
(vi) a point in the exterior
(vii) a sector
(viii) a segment

Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Every diameter of a circle is also a chord.
(ii) Every chord of a circle is also a diameter.
(iii) Two diameters of a circle will necessarily intersect.
(iv) The centre of the circle is always in its interior.
Solution: