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

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:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Check Your Progress

ML Aggarwal Class 6 Solutions Chapter 9 Algebra 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 9 Algebra Check Your Progress

Question 1.
Look at the following matchstick pattern of polygons. Complete the table. Also write the general rule that gives the number of matchsticks.

Solution:

Question 2.
Write an algebraic expression for each of the following:
(i) If 1 metre cloth costs ₹ x, then what is cost of 6 metre cloth?
(ii) If the cost of a notebook is ₹ x and the cost of a book is ₹ y, then what is the cost of 5 notebooks and 2 books?
(iii) The score of Ragni in Mathematics is 23 more than two-third of her score in English. If she scores x marks in English, what is her score in Mathematics?
(iv) If the length of a side of a regular pentagon is x cm, then what is the perimeter of the pentagon?
Solution:

Question 3.
When x = 4 and y = 2, find the value of:
(i) x + y
(ii) x – y
(iii) x2 + 2
(iv) x2 – 2xy + y2
Solution:

Question 4.
When a = 3 and b = -1, find the value of 2a3 – b4 + 3a2b3.
Solution:

Question 5.
When a = 3, b = 0, c = -2, find the values of:
(i) ab + 2bc + 3ca + 4abc
(ii) a3 + b3 + c3 – 3abc
Solution:

Question 6.
Solve the following linear equations:
(i) 2x – $$1 \frac{1}{2}=4 \frac{1}{2}$$
(ii) 3(y – 1) = 2(y + 1)
(ii) n – 3 = 5n + 21
(iv) $$\frac{1}{3}(7 x-1)=\frac{1}{4}$$
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 12 Symmetry Objective Type Questions

ML Aggarwal Class 6 Solutions Chapter 12 Symmetry 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 12 Symmetry Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The subtraction symbol – has …….. lines of symmetry.
(ii) The addition symbol + has …….. lines of …….. symmetry.
(iii) Line of symmetry is also known …….. line or …….. of symmetry.
(iv) A kite has …….. line(s) of symmetry:
(v) A parallelogram has …….. line(s) of symmetry.
(vii) A rectangle is symmetrical about the lines joining the …….. of the opposite sides.
(viii)The number of capital letters of the English alphabet having only vertical line of symmetry is ……..
(ix) The number of capital letters of the English alphabet having only horizontal line of symmetry is ……..
(x) The number of capital letters of the English alphabet having both horizontal and vertical lines of symmetry is ……..
(xi) The digits having two lines of symmetry are …….. and ……..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The letter N has one line of symmetry.
(ii) Every hexagon has six lines of symmetry.
(iii) All right-angled triangles have one line of symmetry.
(iv) A triangle with more than one line of symmetry must be an equilateral triangle.
(v) A line of symmetry divides a figure into two identical parts.
(vi) A circle has only 8 lines of symmetry.
(vii) A regular octagon has 10 lines of symmetry.
(viii) A square and a rectangle have the same number of lines of symmetry.
(ix) A right-angled triangle can have at most one line of symmetry.
(x) If an isosceles triangle has more than one line of symmetry, then it must be rn equilateral triangle.
(xi) If a rectangle has more than two lines of symmetry, then it must be a square.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 15):
Question 3.
The number of lines of symmetry of a scalene triangle is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:

Question 4.
The letter F has
(a) one horizon line of symmetry
(b) one vertical line of symmetry
(c) two lines of symmetry
(d) no line of symmetry
Solution:
no line of symmetry (d)

Question 5.
The number of lines of symmetry of a rectangle is
(a) 0
(b) 1
(c) 2
(d) 4
Solution:

Question 6.
(a) each of its two diagonals
(b) each of its two lines joining the mid-points of opposite sides
(c) each of the perpendicular bisector of its sides
(d) none of these.
Solution:

Question 7.
The number of lines of symmetry of a circle is
(a) 4
(b) 8
(c) 16
(d) unlimited
Solution:

Question 8.
Which of the following letters does not have any line of symmetry?
(a) B
(b) T
(c) Z
(d) Y
Solution:
Z (c)

Question 9.
Which of the following letters does not have the vertical line of symmetry?
(a) A
(b) H
(c) M
(d) E
Solution:

Question 10.
Which figure from the following figures is not symmetrical with respect to any line?

Solution:

Question 11.
In which of the given figures is the dotted line of symmetry?

Solution:

Question 12.
Amongst the given figures, the one having a maximum number of lines of symmetry is:

Solution:

Question 13.
The angle between the mirror line l and the line segment joining a point and its reflection (image) is:
(a) 0°
(b) 45°
(c) 60°
(d) 90°
Solution:
90° (d)

Question 14.
Which of two figures are image of each other (mirror line shown dotted)?

Solution:

Question 15.
Which of the two figures are mirror images of each other (mirror line showed dotted)?

Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 12 Symmetry Ex 12.2

ML Aggarwal Class 6 Solutions Chapter 12 Symmetry Ex 12.2 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 12 Symmetry Ex 12.2

Question 1.
Copy the following figures on a squared paper. Complete each of them such that the dotted line is the line of symmetry:

Solution:

Question 2.
Copy the following figures on a squared paper. Complete each of them such that the resultant figure has two dotted lines as the lines of symmetry:

Solution:

Question 3.
In the given figure, l is the line of symmetry. Complete the diagram to make it symmetrical.

Solution:

Question 4.
In the given figure, l is the line of symmetry. Draw the image of the parallelogram and complete the diagram so that it becomes symmetrical.

Solution:

Question 5.
Copy the following figures on a squared paper and find their reflections in the mirror line l.

Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 12 Symmetry Ex 12.1

ML Aggarwal Class 6 Solutions Chapter 12 Symmetry Ex 12.1 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 12 Symmetry Ex 12.1

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

Solution:

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

Solution:

Question 3.
Draw the line (or lines) of symmetry, if any, of the following road signs and count their number:

Solution:

Question 4.
Draw the line (or lines) of symmetry, if any, of the following numerals and count their number:

Solution:

Question 5.
Copy the following figures on a squared paper and draw the lines of symmetry (if any) and count their number:

Solution:

Question 6.
Write the letters of words ‘JUST LOOK’ which have no line of symmetry.
Solution:

Question 7.
Can you draw a triangle which has
(i) exactly one line of symmetry?
(ii) exactly two lines of symmetry?
(iii) exactly three lines of symmetry?
(iv) no lines of symmetry?
Sketch a rough figure in each case and name the triangle.
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 11 Understanding Symmetrical Shapes Check Your Progress

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes 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 11 Understanding Symmetrical Shapes Check Your Progress

Question 1.
In the given figure, identify the longest and shortest line segments by measuring their lengths.

Solution:

Question 2.
Where will the hour hand of a clock stop if it starts from 10 and turns through 3 right angles?
Solution:
7

Question 3.
Classify the angles whose measures are given below:
(i) 56°
(ii) 125°
(iii) 90°
(iv) 180°
(v) 215°
(vi) 328°
Solution:

Question 4.
Name the types of the following triangles:
(i) ∆ABC with AB = 8 cm, AC = 7 cm and BC = 5.5 cm.
(ii) ∆PQR with PQ = PR = 5 cm and QR = 7.3 cm.
(iii) ∆DEF with D = ∠90°.
(iv) ∆XYZ with ∠Y = 90° and XY = YZ.
(v) ∆LMN with ∠L = 30°, ∠M = 70° and ∠N = 80°.
Solution:

Question 5.
Name each of the following triangles in two different ways (you may use ruler and protractor):

Solution:

Question 6.
State whether the following statements are true or false:
(i) A rectangle is a regular quadrilateral.
(ii) A rhombus is a regular quadrilateral.
(iii) Every parallelogram is a rhombus.
(iv) The diagonals of a rhombus intersect at right angles.
(v) A polygon having 6 sides is called an octagon.
(vi) A road roller has two plane circular faces and one curved face.
(vii) A rectangular pyramid has 5 rectangular faces.
Solution:

Question 7.
Draw a rough sketch of a regular octagon and draw a square by joining exactly four of its vertices.
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 11 Understanding Symmetrical Shapes Objective Type Questions

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes 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 11 Understanding Symmetrical Shapes Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) An angle whose measure is less than that of a right angle is …………
(ii) An angle whose measure is the sum of the measures of two right angles is …………
(iii) When the sum of measures of two angles is that of a right angle, then each on of them is …………
(iv) When the sum of measures of two angles is that of a straight angle and if one of them is acute then the other is …………
(v) A triangle having one of its angles as right angle and with lengths of two sides equal is called ………… triangle.
(vi) A cuboid has ………… faces, ………… edges and ………… vertices.
(vii) A rectangular pyramid has ………… faces, ………… edges and ………… vertices.
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Each angle of an equilateral triangle is a right angle.
(ii) The adjacent sides of a rectangle are equal in length.
(iii) The diagonals of a rectangle are equal in length.
(iv) The diagonals of a rectangle are perpendicular to one another.
(v) The diagonals of a rhombus are equal in length.
(vi) Any three line segments make up a triangle.
(vii) All the faces of a triangular prism are triangles.
(viii)All the faces of a triangular pyramid are triangles.
Solution:

Question 3.
State whether the following statement is true or false. Justify your answer.
‘An angle whose measure is greater than that of a right angle is obtuse’.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (4 to 15):

Question 4.
Comparison of lengths is possible in case of
(a) two lines
(b) two line segments
(c) two rays
(d) a ray and a line segment
Solution:

Question 5.
A reflex angle measures
(a) more than 90° but less than 180°
(b) more than 180° but less than 270°
(c) more than 180° but less than 360°
(d) none of these
Solution:

Question 6.
A scalene triangle cannot be
(a) an acute angled triangle
(b) an obtuse angled triangle
(c) a right angled triangle
(d) an equilateral triangle
Solution:

Question 7.
An obtuse angled triangle can be
(a) right angled
(b) isosceles
(c) equilateral
(d) none of these
Solution:

Question 8.
If you are facing north and turn through $$\frac{3}{4}$$ of a turn in anti-clockwise direction, which direction will you face?
(a) east
(b) south
(c) west
(d) north
Solution:

Question 9.
Open any two adjacent fingers of your hand. What kind of angle you get?
(a) acute
(b) right
(c) obtuse
(d) straight
Solution:

Question 10.
In the given figure, the number of obtuse angles is

(a) 2
(b) 3
(c) 4
(d) 5
Solution:

Question 11.
If the sum of two angles is an obtuse angle, then which of the following is not possible? one right angle and one acute angle one obtuse angle and one acute angle two acute angles two right angles
(a) two right angles
(b) one obtuse angle and one acute angle
(c) two acute angles
(d) two right angles
Solution:

Question 12.
If the sum of two angles is greater than 180°, then which of the following is not possible?
(a) two obtuse angles
(b) two right angles
(c) one obtuse and one acute angle
(d) one reflex and one acute angle
Solution:

Question 13.
Which of the following statements is false?
(a) Every quadrilateral triangle is an isosceles triangle.
(b) Every isosceles triangle is an equilateral triangle.
(c) Every parallelogram is a trapezium.
(d) Every trapezium is a quadrilateral.
Solution:

Question 14.
Which of the following statement is correct?
(a) Every rhombus is a square
(b) Every parallelogram is a rectangle
(c) Every square is a rhombus
(d) Every rectangle is a square
Solution:

Question 15
A quadrilateral whose each angle is a right angle is a
(a) trapezium
(b) parallelogram
(c) rhombus
(d) rectangle
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
If the lengths of two sides of an isosceles triangle are 3 cm and 7 cm, then what is the lengths of the third side?
Solution:

Question 2.
If the lengths of three consecutive sides of an isosceles trapezium are 5 cm, 6 cm and 8 cm, then what is the length of the fourth side?
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 11 Understanding Symmetrical Shapes Ex 11.6

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes Ex 11.6 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 11.6

Question 1.
What is the shape of
(ii) a brick?
(iii) a matchbox?
(iv) a dum?
(v) a playing die?
Solution:

Question 2.
Match the following:

Solution:

Question 3.
Fill in the blanks:
(i) A cube has ……… square faces, ……… edges and ……… vertices.
(ii) A triangular prism has ……… triangular faces, ……… rectangular faces, ……… edges and ……… vertices.
(iii) A triangular pyramid has ……… faces, ……… edges and vertices.
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 11 Understanding Symmetrical Shapes Ex 11.5

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes Ex 11.5 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 11.5

Question 1.
State whether the following statements are true (T) or false (F):
(i) Each angle of a rectangle is a right angle.
(ii) The opposite sides of a rectangle are equal in length.
(iii) The diagonals of a square are perpendicular to one another.
(iv) All sides of a rhombus are equal in length.
(v) All sides of a parallelogram are equal in length.
(vi) The opposite sides of a trapezium are parallel.
(vii) The diagonal of a parallelogram are equal.
Solution:

Question 2.
Examine whether the following figures are polygons. Give reasons.

Solution:

Question 3.
Name each of the following polygons:

Solution:

Question 4.
Draw a rough sketch of a pentagon and draw its diagonals.
Solution:

Question 5.
Draw a rough sketch of a regular hexagon. Connecting three of its vertices draw:
(i) an isosceles triangle
(ii) a light angled triangle.
Solution:

Question 6.
Can you identify the regular quadrilateral?
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 11 Understanding Symmetrical Shapes Ex 11.4

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes Ex 11.4 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 11 Understanding Symmetrical Shapes Ex 11.4

Question 1.
Name the following triangles with regards to sides :

Solution:

Question 2.
Name the following triangles with regards to angles :

Solution:

Question 3.
Name each of the following triangles in two different ways (you may judge the nature of the angle by observation):

Solution:

Question 4.
Match the following:

Solution:

Question 5.
State which of the following statement are true and which are false :
(i) A triangle can have two right angles.
(ii) A triangle cannot have more than one obtuse angle.
(iii) A triangle has atleast two actue angles.
(iv) If all the three sides of a triangle are equal, it is called a scalene triangle.
(v) A triangle has four sides.
(vi) An isosceles triangle is an equilateral triangle also.
(vii) An equilateral triangle is an isosceles triangle also.
(viii)An scalene triangle has all its angles equal.
Solution:

## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 11 Understanding Symmetrical Shapes Ex 11.3

ML Aggarwal Class 6 Solutions Chapter 11 Understanding Symmetrical Shapes Ex 11.3 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 11 Understanding Symmetrical Shapes Ex 11.3

Question 1.
Which of the following are models for perpendicular lines?
(i) The adjacent edges of a postcard.
(ii) the lines of a railway track.
(iii) The line segment forming the letter ‘L’.
(v) The line segments forming the letter ‘V’.
Solution:

Question 2.
In the figure given below, line l is perpendicular to line m.

(a) Is CE = EG?
(b) Does $$\overleftrightarrow { PE }$$ bisect segment $$\overline{\mathrm{BH}}$$ ?
(c) Identify any two line segments for which $$\overleftrightarrow { PE }$$ is the perpendicular bisector.
(d) Are these true?
(i) AC > FG
(ii) CD = GH
(iii) BC < EG.
Solution: