Practical Geometry (Chapter 10), Symmetry (Chapter 14) and Visualising Solid Shapes (Chapter 15)

In each of the Questions 1 to 26, there are four options, out of which one is correct. Choose the correct one.

A triangle can be constructed by taking its sides as:

a.  $1.8\text{ cm},2.6\text{ cm},4.4\text{ cm}$

b. $2\text{ cm},3\text{ cm},4\text{ cm}$ 

c.  $2.4\text{ cm},2.4\text{ cm},6.4\text{ cm}$

d. $3.2\text{ cm},2.3\text{ cm},5.5\text{ cm}$

(b)

Condition for the formation of a triangle is that sum of two sides should be greater than the third side.

Sum of two sides $>$ Third side,

Here, option (b) satisfies the given condition. $\left(2+3\right)\text{cm}>4\text{cm}$ i.e. $5\text{cm}>4\text{cm}$, which holds true.

A triangle can be constructed by taking two of its angles as:

a.    $110°,40°$ 

b.   $70°,115°$ 

c.    $135°,45°$ 

d.   $90°,90°$

(a)

For a triangle, the sum of all interior angles should be equal to $180°$. So, sum of any two angles of a triangle should be less than $180°$

For option (a)

$110°+40°=150°$ i.e. less than $180°$.

For option (b)

$70°+115°=185$ i.e. greater than $180°$.

For option (c)

$135°+45°=180°$ i.e. equal to $180°$.

For option (d)

 $90°+90°=180°$ i.e. equal to $180°$.

So, the correct answer is (a).

The number of lines of symmetry in the figure given below is:

a.  $4$ 

b. $8$ 

c.  $6$ 

d. Infinitely many

(c)

The given figure has 6 lines of symmetry.

The number of lines of symmetry in Fig. 12.14 is

Fig. 12.14

a.  $1$ 

b. $3$

c.  $6$ 

d. Infinitely many

(b)

The given figure has $3$ lines of symmetry.

The order of rotational symmetry in the Fig. 12.15 given below is

Fig. 12.15

a.  $4$ 

b. $8$ 

c.  $6$ 

d. Infinitely many

(c)

Since, the number of times a figure fits onto itself in one full turn is called order of rotational symmetry.

So, for the given figure the order of rotational symmetry is six.

So, the correct answer is (c).

The order of rotational symmetry in the Fig. 12.16 given below is

Fig. 12.16

a.  $4$ 

b. $2$ 

c.  $1$ 

d. Infinitely many

 (b)

 The number of times a figure fits onto itself in one full turn is called order of rotational symmetry. So, the given figure has rotational symmetry of order $2$. Hence, the correct answer is (b).

The name of the given solid in Fig. 12.17 is:

Fig. 12.17

a.  triangular pyramid

b. rectangular pyramid

c.  rectangular prism

d. triangular prism

(b)

In the given figure the base of the pyramid is a rectangle. So, the correct answer is (b).

The name of the solid in Fig. 12.18 is:

Fig. 12.18

a.    triangular pyramid     

b.   rectangular prism

c.    triangular prism      

d.   rectangular pyramid

(c)

A prism always consists of 2 bases which are polygons and faces which are rectangular. This figure has 2 faces which are triangular in shape and can be considered as bases. The rest of the faces are rectangular in shape.

So, the correct answer is (c).

All faces of a pyramid are always:

a.  Triangular

b. Rectangular

c.  Congruent

d. None of these

(d)

The faces of a pyramid can be triangular or rectangular. But we need to choose only one correct answer. So, the correct answer is (d).

A solid that has only one vertex is

a.    Pyramid

b.   Cube

c.    Cone

d.   Cylinder

(c)

From the figure it is clearly seen that the cone shape has only one vertex.

So, the correct answer is (c).

Out of the following which is a 3-D figure?

a.    Square

b.   Sphere

c.    Triangle

d.   Circle

(b)

A 3-D figure is defined as the figure which can be specified in all the three-dimensional axis. A 2-D figure can be represented only on a plane. Hence,

square, triangle and circle are 2-D figures while sphere is the 3-D figure.

So, the correct answer is (b).

Total number of edges a cylinder has

a.    $0$

b.   $1$ 

c.    $2$ 

d.   $3$ 

 (c)

The total number of edges of a cylinder are two.

The figure of cylinder is as follows:

So, the correct answer is (c).

A solid that has two opposite identical faces and other faces as parallelograms is a

a.    prism

b.   pyramid

c.    cone

d.   sphere

 (a)

Among the given shapes, prism is the only figure which has two opposite identical faces and other faces as parallelograms.

The solid with one circular face, one curved surface and one vertex is known as:

a.    cone

b.   sphere

c.    cylinder

d.   prism

(a)

A cone has one circular face, one curved surface and one vertex.

If three cubes each of edge $4\text{ cm}$ are placed end to end, then the dimensions of resulting solid are:

a.    $12\text{ cm}\times 4\text{ cm}\times 4\text{ cm}$ 

b.   $4\text{ cm}\times 8\text{ cm}\times 4\text{ cm}$ 

c.    $4\text{ cm}\times 8\text{ cm}\times 12\text{ cm}$ 

d.   $4\text{ cm}\times 6\text{ cm}\times 8\text{ cm}$ 

(a)

When three cubes are placed end to end, then the resultant figure will be a cuboid. The length of this cuboid is three times the length of the cube. The breadth and height of the cuboid remains same as these are edge of the cube.  

So, the cuboid will have the dimensions $12\text{cm}\times 4\text{cm}\times 4\text{cm}$ 

Hence, the correct answer is (a).

When we cut a corner of a cube as shown in the Fig. 12.19, we get the cut out piece as:

Fig. 12.19

a.    square pyramid

b.   trapezium prism

c.    triangular pyramid

d.   a triangle

(c)

If we cut a corner of a cube, then we get cut-out of a piece in the form of triangular pyramid. So, the correct answer is (c).

If we rotate a right-angled triangle of height $5$ cm and base $3\text{ cm}$ about its height a full turn, we get

a.    cone of height $5\text{ cm}$, base $3\text{ cm}$ 

b.   triangle of height $5\text{ cm}$, base $3\text{ cm}$

c.    cone of height $5\text{ cm}$, base $6\text{ cm}$

d.   triangle of height $5\text{ cm}$, base $6\text{ cm}$

(a)

If we rotate a right-angled triangle of height $5\text{cm}$ and base $3\text{cm}$ about its height a full turn, then we get a cone of height $5\text{cm}$ and base $3\text{cm}$.

If we rotate a right-angled triangle of height $5\text{ cm}$ and base  3 cm about its base, we get:

a.    cone of height $3$ cm and base $3$ cm

b.   cone of height $5$ cm and base $5$ cm

c.    cone of height $5$ cm and base $3$ cm

d.   cone of height $3$ cm and base $5$ cm

 (d)

When we rotate a right-angled triangle of height $5\text{ cm}$ and base $3\text{ cm}$ about its base, we get a cone of height $3\text{ cm}$ and base $5\text{ cm}$.

When a torch is pointed towards one of the vertical edges of a cube, you get a shadow of cube in the shape of

a.    square

b.   rectangle but not a square

c.    circle

d.   triangle

 (b)

When a torch is pointed towards one of the vertical edges of a cube, you get a shadow of cube in the shape of rectangle. Hence, the correct answer is (b).

Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle:

a.    $3\text{ cm},4\text{ cm},6\text{ cm}$ 

b.   $9\text{ cm},16\text{ cm},26\text{ cm}$ 

c.    $1.5\text{ cm},3.6\text{ cm},3.9\text{ cm}$ 

d.   $7\text{ cm},24\text{ cm},26\text{ cm}$ 

 (c)

For a right-angled triangle, minimum condition to be satisfied is the Pythagoras theorem which is stated mathematically as below:

(Hypotenuse)² $=$ (Base)² $+$  (Perpendicular)²

So let us try each and every option,

a.  ${\left(6\right)}^2 =36$
${(3)}^2 +{\left(4\right)}^2=25$
$36\ne 25$

b. ${(26)}^2 =676$ 
${(16)}^2 +{\left(9\right)}^2=256+81$ 
$676\ne 337$ 

c.  ${\left(3.9\right)}^2 =15.21$ 
${(1.5)}^2 +{\left(3.6\right)}^2 =2.25+12.96$ 
$15.21=15.21$ (True)

d. ${(26)}^2 ={(7)}^2 +{(24)}^2$
$676\ne 49+576$ 
Hence, option (c) is the correct answer.

In which of the following cases, a unique triangle can be drawn

a.    $\text{AB}=4\text{ cm}$,    $\text{BC}=8\text{ cm}$ and  $\text{CA}=2\text{ cm}$ 

b.   $\text{BC}=5.2\text{ cm}$,    $\angle \text{B}=90°$  and  $\angle \text{C}=110°$ 

c.    $\text{XY}=5\text{ cm}$,    $\angle \text{X}=45°$   and  $\angle \text{Y}=60°$ 

d.   An isosceles triangle with the length of each equal side $6.2$ cm.

 (c)

Let us draw the triangle according to measurements given in respective options.

For (a), As we can see triangle cannot be drawn

For (b), Triangle cannot be formed.

 

For (c), Unique triangle can be drawn by these measurements.

For (d), Using given data, we can form as many triangles as we want.

So, the correct answer is (c).

Which of the following has a line of symmetry?

a.   

b.  

c.   

d.  

 

 

 (c)

The line of symmetry is a line which divides a figure into two equal halves which are mirror image of each other.

The following figure has one line of symmetry

Which of the following are reflections of each other?

a.     

b.    

c.     

d.    

 

 

 (a)

Reflection means the figure should be just in opposite orientation like the image in a mirror, that is the image is just flipped.

Since in the figure (a) the image of one side of the figure is exactly same as the figure on the other side of the line of symmetry.

So, the correct answer is (a).

Which of these nets is a net of a cube?

a.     

b.    

c.     

d.    

 

 

 

 (b)

A net is 2-D figure which when folded in a particular axis gives a 3-D figure.

So, for the net to form a cube, the shape of the interlinking blocks of nets should be a square which is present only in option ‘b’.

Which of the following nets is a net of a cylinder?

a.   

b.    

c.     

d.    

 

 

 

 (c)

A net is 2-D figure which when folded in a particular axis gives a 3-D figure. So for the net to form a cylinder, the shape of the interlinking blocks of nets should contain a rectangle which is present only in option C.

 

Which of the following letters of English alphabets have more than $2$ lines of symmetry?

a. Z

b. O

c. E

d. H

 

 

 

 (b) and (d)

           

 

The letter O has more than two lines of symmetry and letter H has exactly two lines of symmetry.

Take a square piece of paper as shown in figure (1). Fold it along its diagonals as shown in figure (2). Again fold it as shown in figure (3). Imagine that you have cut off 3 pieces of the form of congruent isosceles right-angled triangles out of it as shown in figure 4.

(1)             

 

(2)             

 

 

(3)             

 

 

(4)             

 

 

On opening the piece of paper which of the following shapes will you get?

a.     

b.    

c.     

d.    

 

 

 

 (a)

As per the given steps in the question, if we open the piece of paper, we will get the figure as shown in option (a).

Which of the following 3-dimensional figures has the top, side and front as triangles?

a.     

b.    

c.     

d.    

 

 

 

 (c)

Figure in option (c) shows all (top, side and front) views as triangle.

 

In Questions 29 to 58, fill in the blanks to make the statements true.

In an isosceles right triangle, the number of lines of symmetry is ________.

One

Since, an isosceles triangle has one line of symmetry drawn from the vertex touching the base as shown in the figure.

 

Rhombus is a figure that has ______ lines of symmetry and has a rotational symmetry of order _______.

two, two

A rhombus has two lines of symmetry along the diagonal and has a rotational symmetry of order two.

__________ triangle is a figure that has a line of symmetry but lacks rotational symmetry.

Isosceles

The triangle which has only one line of symmetry and no rotational symmetry is the isosceles triangle.

An isosceles triangle is a figure that has a line of symmetry but lacks rotational symmetry.

__________ is a figure that has neither a line of symmetry nor a rotational symmetry.

Scalene Triangle

Scalene Triangle has all sides unequal and hence it has no lines of symmetry or rotational symmetry.

Scalene Triangle is a figure that has neither a line of symmetry nor a rotational symmetry.

 

__________ and __________ are the capital letters of English alphabets that have one line of symmetry but they interchange to each other when rotated through $180°$.

 

 

M, W

The only two letters which have only one line of symmetry and those which interchange to each other when rotated through 180° are M and W.

The common portion of two adjacent faces of a cuboid is called __________.

Edge

The common portion of two adjacent faces of a cuboid is called edge.

A plane surface of a solid enclosed by edges is called __________ .

Face

A plane surface of a solid enclosed by edges is called face.

The corners of solid shapes are called its __________.

Vertices

The corners of solid shapes are called its vertices.

A solid with no vertex is __________.

Sphere

Since, a sphere is a solid with $0$ vertex, $0$ edge and $1$ curved surface,

A triangular prism has __________ faces, __________ edges and__________ vertices.

$5,9,6$

A triangular prism has $5$ faces, $9$ edges and $6$ vertices.

A triangular pyramid has __________ faces, __________ edges and __________vertices.

$4,6,4$

A triangular pyramid has $4$ faces, $6$ edges and $4$ vertices.

A square pyramid has __________ faces, __________ edges and__________ vertices.

$5,8,\text{ 5}$

A square pyramid has $5$ faces, $8$ edges and $5$ vertices.

Out of __________ faces of a triangular prism, __________are rectangles and __________ are triangles.

Out of $5$ faces of a triangular prism, $3$ are rectangles and $2$ are triangles.

The base of a triangular pyramid is a __________.

Triangle

The base of a triangular pyramid is a triangle.

Out of __________ faces of a square pyramid, __________ are triangles and __________ is/are squares.

Out of $5$ faces of a square pyramid, $4$ are triangles and $1$ is square.

Out of __________ faces of a rectangular pyramid __________ are triangles and base is __________.

Out of $5$ faces of a rectangular pyramid, $4$ are triangles and base is rectangle

Each of the letters H, N, S and Z has a rotational symmetry of order__________.

2

Each of the letters H, N, S and Z has a rotational symmetry of order two.

Order of rotational symmetry of a rectangle is __________.

Order of rotational symmetry of a rectangle is two.

 

 

Order of rotational symmetry of a circle is __________.

Order of rotational symmetry of a circle is infinite.

The number of times a figure fits onto itself in one complete rotation is called the order of rotational symmetry.

 

Each face of a cuboid is a __________.

A cuboid is a solid figure which is bounded by six rectangular faces.

 

 

$\therefore$ Each face of a cuboid is a rectangle.

Line of symmetry for an angle is its __________.

Line of symmetry for an angle is its bisector.

A parallelogram has __________ line of symmetry.

A parallelogram has no line of symmetry.

Order of rotational symmetry of  is _________.

8

The number of times a figure fits into itself in one full turn is called as order of rotational symmetry.

$\therefore$ Order of rotational symmetry of a given figure is $8$.

A __________ triangle has no lines of symmetry.

Scalene

A scalene triangle has no lines of symmetry. Since, all of its angles and sides are of unequal length.

Cuboid is a rectangular_________ .

Prism

Rectangular prism and cuboid are same solids.

A sphere has __________vertex, __________edge and __________curved surface.

A sphere has zero vertex, zero edge and $1$ curved surface.

 is a net of a ______.

 

 

→ Circumference of circle $=$ ______.

Cone

 

 

→ Circumference of circle $=$$2\text{πr}$ 

 is a net of a __________.

Order of rotational symmetry of  is _____.

$1$

For the given triangle, two sides are equal which means it is an isosceles triangle.

Since, isosceles triangle has rotational symmetry of order $1$.

Identical cubes are stacked in the corner of a room as shown below. The number of cubes that are not visible are _________.

 

 

 

$20$ 

The number of cubes that are not visible are $20$.

 

In Questions from 59 to 92, state whether the statements are True or False.

We can draw exactly one triangle whose angles are $70°$, $30°$ and $80°$.

False

The sum of the angles given is $70°$ + $30°$ + $80°$  $=180°$.Though the angles are unique for the triangle, but the length of the sides can differ and hence the number of triangles that can be drawn with these angles will also be infinite.

The distance between the two parallel lines is same everywhere.

True

The distance between the two parallel lines is always same everywhere.

A circle has two lines of symmetry.

False

A circle has infinite lines of symmetry.

An angle has two lines of symmetry.

False

An angle has only one line of symmetry i.e. its bisector.

A regular hexagon has six lines of symmetry.

True

A regular polygon has many lines of symmetry equal to the number of its sides.

An isosceles trapezium has one line of symmetry.

True

Isosceles trapezium has only one line of symmetry along the line segment joining the mid-points of two parallel sides which is shown in figure.

A parallelogram has two lines of symmetry.

False

A parallelogram has no lines of symmetry. So the given statement is false.

Order of rotational symmetry of a rhombus is four.

False

Order of rotational symmetry of a rhombus is two, so the given statement is false.

An equilateral triangle has six lines of symmetry.

False

Since, in an equilateral triangle, there are three lines of symmetry along the three medians of the triangle.

Order of rotational symmetry of a semi-circle is two.

False

Order of rotational symmetry of a semi-circle is one.

In oblique sketch of the solid, the measurements are kept proportional.

False

In oblique sketch of the solid, the measurements are not kept proportional. So, the given statement is false.

An isometric sketch does not have proportional length.

 

False

An isometric sketch always has proportional length.

So, the given statement is false.

A cylinder has no vertex.

True

A cylinder has $3$ faces, $2$ edges but no vertex. Hence, the statement is true.

All the faces, except the base of a square pyramid are triangular.

True

A square pyramid has $4$ triangular faces and one square base. So, the given statement is true.

A pyramid has only one vertex.

False

A pyramid has at least $4$ vertices (in triangular pyramid). So, the given statement is false.

A triangular prism has $5$ faces, $9$ edges and $6$ vertices.

True

 

A triangular prism has $5$ faces, $9$ edges and $6$ vertices.

If the base of a pyramid is a square, it is called a square pyramid.

True

The name of a pyramid is based on the base of pyramid. So, if the base of a pyramid is a square, then it is called a square pyramid.

A rectangular pyramid has $5$ rectangular faces.

False

A rectangular pyramid has $1$ rectangular face and $4$ triangular faces.

Rectangular prism and cuboid refer to the same solid.

True

Rectangular prism and cuboid refer to the same solid.

A tetrahedron has $3$ triangular faces and $1$ rectangular face.

False

A tetrahedron has 4 triangular faces.

While rectangle is a 2-D figure, cuboid is a 3-D figure.

True

A rectangle is a 2-D figure and cuboid is a 3-D figure.

While sphere is a 2-D figure, circle is a 3-D figure.

False

Circle is a 2-D figure and sphere is a 3-D figure

Two dimensional figures are also called plane figures.

True

2-D figures are also called plane figures. So, the statement is true.

A cone is a polyhedron.

False

A cone is not a polyhedron.

A prism has four bases.

False

A prism has twobases.

The number of lines of symmetry of a regular polygon is equal to the vertices of the polygon.

True

The number of lines of symmetry of a regular polygon is equal to the vertices of the polygon. So, the statement is true.

The order of rotational symmetry of a figure is $4$ and the angle of rotation is $180°$ only.

False

If the order of rotational symmetry of a figure is $4$, then the angle of rotation must be $90°$.

After rotating a figure by $120°$ about its centre, the figure coincides with its original position. This will happen again if the figure is rotated at an angle of $240°$.

True

After rotating a figure by $120°$ about its centre, the figure coincides with its original position. This will happen again, if the figure is rotated at an angle of $240°$.

Mirror reflection leads to symmetry always.

False

Mirror reflection does not always lead to symmetry.

Rotation turns an object about a fixed point which is known as centre of rotation.

True

Centre of rotation turns an object about a fixed point.

Isometric sheet divides the paper into small isosceles triangles made up of dots or lines.

False

Isometric sheet divides the paper into small equilateral triangles made up of dots or lines. So, the statement is false.

The circle, the square, the rectangle and the triangle are examples of plane figures.

True

The circle, the square, the rectangle and the triangle are examples of plane figures.

The solid shapes are of two-dimensional.

False

The solid shapes are of three-dimensional.

Triangle with length of sides as $5$ cm, $6$ cm and $11\text{ cm}$ can be constructed.

False

We know that, in a triangle, sum of any two sides is always greater than the third side.

$5+6=11$ 

Here, the sum of two sides is equal to the third side.

Hence, these measurements do not satisfy the basic condition of a triangle. Hence, the triangle cannot be constructed.

Draw the top, side and front views of the solids given below in

(1)             

(2)             

 

 

 

For given Fig. (1)

 

 

For given Fig. (2)

 

Draw a solid using the top. side and front views as shown below. [Use Isometric dot paper].

 

 

 

 

 

 

Construct a right-angled triangle whose hypotenuse measures $5$ cm and one of the other sides measures $3.2$ cm.

Steps of construction

Step I: Draw a line $\text{AB of side}=3.2\text{ cm}\text{.}$

Step II: Construct a right angle ( $90°$ ) at point B and draw a ray BY through it.

Step III: From point A draw and arc of length 5 cm cutting BY at C.

Step IV: Join AC

Step V:  ABCis the required triangle.

 

Construct a right-angled isosceles triangle with one side (other than hypotenuse) of length $4.5$ cm.

Steps of construction

Step I: Draw a line AB of side $4.5\text{cm}\text{.}$ 

Step II: Construct a right angle at point B and draw a ray BY through it.

Step III: From point B, draw an arc of length $4.5\text{ cm}$ cutting BY at C.

Step IV: Join AC

Step V: ABC is the required triangle.

Draw two parallel lines at a distance of $2.2$ cm apart.

Steps of construction are as follows:

Step I: Draw a line $l$ of any length and mark a point $\text{C}$ outside it.

Step II: Take a point B on line $l$ and join BC.

Step III: Draw line parallel to line $l$ passing through C.

Step IV: Mark a point D on line $m$, at a distance of $2.2\text{ cm}$ from C.

Step V: Through D draw $\text{AD}\left|\right|\text{BC}.$ Line $l$ is parallel to line $m$ .

Also, $\text{AD}\left|\right|\text{BC},\text{ AB}=\text{DC}=2.2\text{ cm}$ 

Draw an isosceles triangle with each of equal sides of length $3$ cm and the angle between them as $45°$.

Steps of construction

Step I: Firstly, we draw a rough sketch of triangle with given measures marked on it.

Step II: Draw a line segment AB of length $3\text{ cm}$.

Step III: Draw an angle of $45°$ at point B and produce it to form ray BY.

Step IV: With B as centre, draw an arc of $3\text{ cm}$ which intersects ray BY at C.

Step V: Join AC.

Thus, $\Delta \text{ABC}$ is the required isosceles triangle.

Draw a triangle whose sides are of lengths $4\text{ cm},5\text{ cm}$ and $7$ cm.

Let us assume that given sides are $\text{BC}=7\text{ cm,}$ $\text{AC}=4\text{ cm}$ and $\text{AC}=5\text{ cm}$ 

Steps of construction

Step I: Draw a line segment $\text{BC}=7\text{ cm}$ 

Step II: With centre B and radius $4$ cm draw an arc.

Step III: With centre C and radius $5\text{ cm}$, draw an arc which cuts the previous arc at A.

Step IV: Join AB and AC.

So, $\Delta \text{ABC}$ is the required triangle in which $\text{AB}=4\text{ cm}$, $\text{BC}=7\text{ cm}$ and

$\text{AC}=5\text{ cm}$ 

Construct an obtuse angled triangle which has a base of $5.5\text{ cm}$ and base angles of $30°$ and $120°$.

Steps of construction

Step I: Draw a line segment BC of length $5.5\text{ cm}$ .

Step II: Draw an angle of $120°$ at point B and produce it to form ray BY.

Step III: Draw an angle of $30°$ at point C and produce it to form ray CX.

Step IV: Extend BY and CX in such manner that they intersect to get the third point A.

Step V: Join AC to complete the triangle.

Construct an equilateral triangle ABC of side $6\text{ cm}$.

Steps of construction

Step I: Draw a line segment AB $=6$ cm

Step II: Draw an arc of radius $6$ cm from point A.

Step III: Now, draw another arc of radius $6$ cm from point B to cut previous arc at C.

Step IV: Join A to C and B to C.

So, $\angle \text{ABC}$ is the required triangle.

By what minimum angle does a regular hexagon rotate so as to coincide with its original position for the first time?

A regular hexagon must be rotated through a minimum angle of $60°$. So, that it can coincide with its original position for the first time. Because the angle of rotation of hexagon

$\frac{360°}{\text{Number of sides}}=\frac{360°}{6} =60°$ 

In each of the following figures, write the number of lines of symmetry and order of rotational symmetry.

Fig. 12.23

[Hint: Consider these as 2-D figures not as 3-D objects.]

Figure	No. of lines of symmetry	Order of rotational symmetry
A	1	1
B	1	1
C	1	1
D	2	2
E	1	1
F	0	2
G	1	1
H	0	3
I	4	4
J	1	1
K	0	1
L	1	1
M	0	2
N	0	1
O	1	1
P	0	1
Q	5	5
R	0	1
S	3	3
T	1	1
U	0	10
V	3	3
W	0	1

In the Fig. 12.24 of a cube,

 

 

Fig. 12.24

(1)   Which edge is the intersection of faces EFGH and EFBA?

(2)   Which faces intersect at edge FB?

(3)   Which three faces form the vertex A?

(4)   Which vertex is formed by the faces ABCD, ADHE and CDHG?

(5)   Give all the edges that are parallel to edge AB.

(6)   Give the edges that are neither parallel nor perpendicular to edge BC.

(7)   Give all the edges that are perpendicular to edge AB.

(8)   Give four vertices that do not all lie in one plane.

(1)   From the given figure, we can observe that EF is the intersection of faces EFGH and EFBA.

(2)   From the given figure, we can observe that faces EFBA and FBCG intersect at edge FB.

(3)   Faces ABFE, ADHE and ABCD form the vertex A,

(4)   Vertex D is formed by the faces ABCD, CDHG and ADHE.

(5)   The edges parallel to edge AB are CD, EF and HG.

(6)   From the given figure, we can observe that edges AE, EF, GH and HD are neither parallel nor perpendicular to edge BC.

(7)   From the given figure, we can observe that edges AE, BF, AD and BC are perpendicular to edge AB.

(8)   Vertices A, B, G and H do not lie in one plane.

Draw a net of a cuboid having same breadth and height, but length double the breadth.

Required net of a cuboid will be

Draw the nets of the following:

(i)             Triangular prism

(ii)         Tetrahedron

(iii)      Cuboid

(i)        Net for triangular prism

(ii)         Net for tetrahedron,

(iii) Net for cuboid,

Draw a net of the solid given in the Fig. 12.25:

 

 

Fig. 12.25

 

 

The net of the given solid figure will be

Draw an isometric view of a cuboid $6\text{ cm}\times 4\text{ cm}\times 2\text{ cm}$.

Isometric view of a cuboid $=6\text{ cm}\times 4\text{ cm}\times 2\text{ cm}$ $=l\times b\times h.$

 

The net given below in Fig. 12.26 can be used to make a cube.

 

Fig. 12.26

 

 

(1)     Which edge meets AN?

(2)     Which edge meets DE?

(1)      The given net of a cube shows that edge GH meets edge AN.

(2)      The given net of a cube shows that edge DC meets edge DE.

Draw the net of triangular pyramid with base as equilateral triangle of side $3$ cm and slant edges $5$ cm.

The net of such triangular pyramid will be

Draw the net of a square pyramid with base as square of side $4$ cm and slant edges $6$ cm.

The net of such square pyramid will be

Draw the net of rectangular pyramid with slant edge $6$ cm and base as rectangle with length $4$ cm and breadth $3$ cm.

The net of such rectangular pyramid will be

Find the number of cubes in each of the following figures and in each case give the top, front, left side and right side view (arrow indicating the front view).

a.   

b.  

c.   

d.  

e.  

f.    

g.   

h.  

 

 

 

 

 

 

 

a.    The no. of cubes in the given figure is $6$

 

b.   The no. of cubes in the given figure is $8$

 

c.    The no. of cubes in the given figure is $7$

 

d.    

e.     

f.      

g.    

h.    

 

 

Draw all lines of symmetry for each of the following figures as given below:

a.   

b.  

c.   

 

 

a. 

 

1 line of symmetry

b.  

 

No line of symmetry

c.   

 

2 lines of symmetry

How many faces does Fig. 12.27 have?

 

 

Fig. 12.27

There are total $16$ faces in the given figure.

Trace each figure. Then draw all lines of symmetry, if it has.

a.   

b.  

c.   

 

 

 

How many faces does figure have?

a.   

b.  

c.   

 

 

Tell whether each figure has rotational symmetry or not.

a.   

 

b.  

 

 

c.   

 

 

d.  

 

e.  

 

 

f.    

 

 

 

 

a.    Yes

b.   No

c.    No

d.   Yes

e.    Yes

f.Yes

Draw all lines of symmetry for each of the following figures.

a. 

 

b.  

 

 

c.   

 

 

 

d.  

 

e.  

 

 

 

 

f.    

 

 

 

a. 

b.

c. 

d.

e.

f.  

 

 

 

Tell whether each figure has rotational symmetry. Write yes or no.

a.     

b.    

c.     

d.    

 

 

 

 

a.    Yes

b.   Yes

c.    No

d.   Yes

Does the Fig. 12.28 have rotational symmetry?

Fig. 12.28

The given figure does not show rotational symmetry because one part of design is undarkened, whereas other three part are darkened. Hence, the design does not show symmetry.

The flag of Japan is shown below. How many lines of symmetry does the flag have?

The given flag has 2 lines of symmetry

Which of the figures given below have both line and rotational symmetry?

a.     

 

b.    

 

 

c.     

 

 

d.    

 

 

 

 

Only (a) has both line & rotational symmetries. In the given figure,

Also, rotational symmetry will be shown as

 

$\frac{360°}{8}=45°,$ i.e, rotational angel is equal to $45°$ 

Which of the following figures do not have line symmetry?

a.     

 

 

b.    

 

 

c.     

 

 

d.    

 

 

 

a.    We observe that the given figure has 2 lines of symmetry

b.   The given figure has one line of symmetry.

c.    We observe that the given figure has 2 lines of symmetry.

d.   The given figure has no line of symmetry.

Which capital letters of English alphabet have no line of symmetry?

The letters F, G, J, L, N,P,  Q, R, S and Z have no line of symmetry.