Math Ncert Exemplar 2019 Solutions for Class 7 Maths Chapter 12 Practical Geometry Symmetry & Visualising Solid Shapes are provided here with simple step-by-step explanations. These solutions for Practical Geometry Symmetry & Visualising Solid Shapes are extremely popular among class 7 students for Maths Practical Geometry Symmetry & Visualising Solid Shapes Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Math Ncert Exemplar 2019 Book of class 7 Maths Chapter 12 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Math Ncert Exemplar 2019 Solutions. All Math Ncert Exemplar 2019 Solutions for class 7 Maths are prepared by experts and are 100% accurate.
Page No 364:
Question 1:
In the given question, 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 cm, 2.6 cm, 4.4 cm
(b) 2 cm, 3 cm, 4 cm
(c) 2.4 cm, 2.4 cm, 6.4 cm
(d) 3.2 cm, 2.3 cm, 5.5 cm
Answer:
We know that
A triangle be constructed if it satisfies the condition.
The sum of two sides is greater than the third side.
(a) 1.8 + 2.6 = 4.4
Here 4.4 is not greater than 4.4
(b) 2 + 3 = 5
5 > 4
Here 5 is greater than 4
(c) 2.4 + 2.4 = 4.4
Here 4.4 is less than 6.4
(d) 3.2 + 2.3 = 5.5
Here 5.5 is equal to 5.5
Therefore, a triangle can be constructed by taking its sides as 2 cm, 3 cm, 4 cm.
Page No 364:
Question 2:
In the given question, there are four options, out of which one is correct. Choose the correct one.
A triangle can be constructed by taking two of its angles as:
(a) 110°, 40°
(b) 70°, 115°
(c) 135°, 45°
(d) 90°, 90°
Answer:
Page No 364:
Question 3:
In the given question, there are four options, out of which one is correct. Choose the correct one.
The number of lines of symmetry in the figure given below is:
(a) 4
(b) 8
(c) 6
(d) Infinitely many.
Answer:
The number of lines of symmetry in the figure given below is 8.
Page No 365:
Question 4:
In the given question, there are four options, out of which one is correct. Choose the correct one.
The number of lines of symmetry in given figure is
figure
(a) 1
(b) 3
(c) 6
(d) Infinitely many
Answer:
ans
Page No 365:
Question 5:
In the given question, there are four options, out of which one is correct. Choose the correct one.
The order of rotational symmetry in the figure given below is
(a) 4
(b) 8
(c) 6
(d) Infinitely many
Answer:
The order of rotational symmetry in the figure given below is 6.
Page No 365:
Question 6:
In the given question, there are four options, out of which one is correct. Choose the correct one.
The order of rotational symmetry in the figure given below is
(a) 4
(b) 2
(c) 1
(d) Infinitely many.
Answer:
The order of rotational symmetry in the figure given below is 2.
Page No 365:
Question 7:
In the given question, there are four options, out of which one is correct. Choose the correct one.
The name of the given solid in figure is:
(a) triangular pyramid
(b) rectangular pyramid
(c) rectangular prism
(d) triangular prism
Answer:
The name of the given solid in figure is rectangular pyramid.
Page No 366:
Question 8:
In the given question, there are four options, out of which one is correct. Choose the correct one.
The name of the solid in figure is:
(a) triangular pyramid
(b) rectangular prism
(c) triangular prism
(d) rectangular pyramid
Answer:
The name of the solid in figure is triangular prism.
Page No 366:
Question 9:
In the given question, there are four options, out of which one is correct. Choose the correct one.
All faces of a pyramid are always:
(a) Triangular
(b) Rectangular
(c) Congruent
(d) None of these
Answer:
The faces of pyramid can be rectangular or triangular.
So, none of these is the answer.
Page No 366:
Question 10:
In the given question, there are four options, out of which one is correct. Choose the correct one.
A solid that has only one vertex is
(a) Pyramid
(b) Cube
(c) Cone
(d) Cylinder
Answer:
A solid that has only one vertex is pyramid.
Page No 366:
Question 11:
In the given question, there are four options, out of which one is correct. Choose the correct one.
Out of the following which is a 3-D figure?
(a) Square
(b) Sphere
(c) Triangle
(d) Circle
Answer:
Out of the given figure sphere is a 3-D figure.
Page No 366:
Question 12:
In the given question, there are four options, out of which one is correct. Choose the correct one.
Total number of edges a cylinder has
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
Total number of edges a cylinder is 0.
Page No 366:
Question 13:
In the given question, there are four options, out of which one is correct. Choose the correct one.
A solid that has two opposite identical faces and other faces as parallelograms is a
(a) prism
(b) pyramid
(c) cone
(d) sphere
Answer:
A solid that has two opposite identical faces and other faces as parallelograms is a prism.
Page No 366:
Question 14:
In the given question, there are four options, out of which one is correct. Choose the correct one.
The solid with one circular face, one curved surface and one vertex is known as:
(a) cone
(b) sphere
(c) cylinder
(d) prism
Answer:
The solid with one circular face, one curved surface and one vertex is known as a cone.
Page No 366:
Question 15:
In the given question, there are four options, out of which one is correct. Choose the correct one.
If three cubes each of edge 4 cm are placed end to end, then the dimensions of resulting solid are:
(a) 12 cm × 4 cm × 4 cm
(b) 4 cm × 8 cm × 4 cm
(c) 4 cm × 8 cm × 12 cm
(d) 4 cm × 6 cm × 8 cm
Answer:
If three cubes each of edge 4 cm are placed end to end, then the dimensions of resulting solid are 12 cm × 4 cm × 4 cm.
Page No 367:
Question 16:
In the given question, there are four options, out of which one is correct. Choose the correct one.
When we cut a corner of a cube as shown in the figure we get the cutout piece as :
(a) square pyramid
(b) trapezium prism
(c) triangular pyramid
(d) a triangle
Answer:
When we cut a corner of a cube as shown in the figure we get the cutout piece as a triangular pyramid.
Hence, the correct answer is (c).
Page No 367:
Question 17:
In the given question, there are four options, out of which one is correct. Choose the correct one.
If we rotate a right-angled triangle of height 5 cm and base 3 cm about its height a full turn, we get
(a) cone of height 5 cm, base 3 cm
(b) triangle of height 5 cm, base 3 cm
(c) cone of height 5 cm, base 6 cm
(d) triangle of height 5 cm, base 6 cm
Answer:
If we rotate a right-angled triangle of height 5 cm and base 3 cm about its height a full turn, we get cone of height 5 cm, base 3 cm
Change the colour
Hence, the correct answer is option (a).
Page No 367:
Question 18:
In the given question, there are four options, out of which one is correct. Choose the correct one.
If we rotate a right-angled triangle of height 5 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
Answer:
If we rotate a right-angled triangle of height 5 cm and base 3 cm about its base, we get a cone of height 3 cm and base 5 cm.
Change the colour
Hence, the correct answer is option (d).
Page No 367:
Question 19:
In the given question, there are four options, out of which one is correct. Choose the correct one.
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
Answer:
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 but not a square.
Hence, the correct answer is option (b).
Page No 367:
Question 20:
In the given question, there are four options, out of which one is correct. Choose the correct one.
Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle:
(a) 3 cm, 4 cm, 6 cm
(b) 9 cm, 16 cm, 26 cm
(c) 1.5 cm, 3.6 cm, 3.9 cm
(d) 7 cm, 24 cm, 26 cm
Answer:
1.5 cm, 3.6 cm, 3.9 cm
From the Pythagoras theorem,
Hypotenuse2 = base2 + height2
(3.9)2 = (1.5)2 + (3.6)2
15.21 = 2.25 + 12.96
15.21 = 15.21
Thus, the lengths 1.5 cm, 3.6 cm, 3.9 cm are the sides of a right-angled triangle.
Hence, the correct answer is option (c).
Page No 368:
Question 21:
In the given question, there are four options, out of which one is correct. Choose the correct one.
In which of the following cases, a unique triangle can be drawn
(a) AB = 4 cm, BC = 8 cm and CA = 2 cm
(b) BC = 5.2 cm, ∠B = 90° and ∠C = 110°
(c) XY = 5 cm, ∠X = 45° and ∠Y = 60°
(d) An isosceles triangle with the length of each equal side 6.2 cm.
Answer:
A unique triangle can be drawn if two angles and one-side measurements are given.
Thus, a unique triangle can be drawn with the measurements XY = 5 cm, ∠X = 45° and ∠Y = 60°. As there are two acute angles given with the length of one side between them.
Hence, the correct answer is option (c).
Page No 368:
Question 22:
In the given question, there are four options, out of which one is correct. Choose the correct one.
Which of the following has a line of symmetry?
(a)
(b)
(c)
(d)
Answer:
The figure in option (c) has a line of symmetry.
Hence, the correct answer is option (c).
Page No 368:
Question 23:
In the given question, there are four options, out of which one is correct. Choose the correct one.
Which of the following are reflections of each other?
Answer:
A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
In option (a) the figures given show the reflection of each other.
Hence, the correct answer is option (a).
Page No 368:
Question 24:
In the given question, there are four options, out of which one is correct. Choose the correct one.
Which of these nets is a net of a cube?
(a)
(b)
(c)
(d)
Answer:
The net given in option (b) is the net of the cube.
Change the colour
Hence, the correct answer is option (b).
Page No 368:
Question 25:
In the given question, there are four options, out of which one is correct. Choose the correct one.
Which of the following nets is a net of a cylinder?
(a)
(b)
(c)
(d)
Answer:
The net given in option (c) is the net of the cylinder.
Change the colour
Hence, the correct answer is option (c).
Page No 368:
Question 26:
In the given question, there are four options, out of which one is correct. Choose the correct one.
Which of the following letters of English alphabets have more than 2 lines of symmetry?
(a)
(b)
(c)
(d)
Answer:
Option (a)
Alphabet Z has no line of symmetry.
Option (b)
Alphabet O has infinite lines of symmetry.
Option (c)
Alphabet E has no line of symmetry.
Option (d)
Alphabet H has exact two lines of symmetry.
Thus, alphabet O has more than 2 lines of symmetry.
Hence, the correct answer is option (b).
Page No 368:
Question 27:
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.
On opening the piece of paper which of the following shapes will you get?
Answer:
On opening the piece of paper we will get the shape given in the option (a).
Figure of option (a) in the question.
Hence, the correct answer is option (a).
Page No 369:
Question 28:
Which of the following 3-dimensional figures has the top, side and front as triangles?
Answer:
The figure in option (c) has the top, side and front as triangles.
Hence, the correct answer is option (c).
Page No 369:
Question 29:
Fill in the blanks to make the statements true
In an isosceles right triangle, the number of lines of symmetry is ________.
Answer:
In an isosceles right triangle, the number of lines of symmetry is one.
Change the colour
Page No 369:
Question 30:
Fill in the blanks to make the statements true
Rhombus is a figure that has ______lines of symmetry and has a rotational symmetry of order _______.
Answer:
Rhombus is a figure that has two lines of symmetry and has a rotational symmetry of order 2.
Change the colour
Page No 369:
Question 31:
Fill in the blanks to make the statements true
__________ triangle is a figure that has a line of symmetry but lacks rotational symmetry.
Answer:
Isosceles triangle is a figure that has a line of symmetry but lacks rotational symmetry.
Change the colour
Page No 369:
Question 32:
Fill in the blanks to make the statements true
__________ is a figure that has neither a line of symmetry nor a rotational symmetry.
Answer:
Scalene triangle is a figure that has neither a line of symmetry nor a rotational symmetry.
Page No 370:
Question 33:
Fill in the blanks to make the statements true
__________ and __________ are the capital letters of English alphabets that have one line of symmetry but they interchange to each other when rotated through 180°.
Answer:
M and W are the capital letters of English alphabets that have one line of symmetry but they interchange to each other when rotated through 180°.
Page No 370:
Question 34:
Fill in the blanks to make the statements true
The common portion of two adjacent faces of a cuboid is called __________.
Answer:
The common portion of two adjacent faces of a cuboid is called edge.
Change the colour
Page No 370:
Question 35:
Fill in the blanks to make the statements true
A plane surface of a solid enclosed by edges is called __________ .
Answer:
A plane surface of a solid enclosed by edges is called a face.
Page No 370:
Question 36:
Fill in the blanks to make the statements true
The corners of solid shapes are called its __________.
Answer:
The corners of solid shapes are called its vertices.
Page No 370:
Question 37:
Fill in the blanks to make the statements true
A solid with no vertex is __________.
Answer:
A solid with no vertex is sphere.
Page No 370:
Question 38:
Fill in the blanks to make the statements true
A triangular prism has __________ faces, __________ edges and __________ vertices.
Answer:
A triangular prism has 5 faces, 9 edges and 6 vertices.
Change the colour
Page No 370:
Question 39:
Fill in the blanks to make the statements true
A triangular pyramid has __________ faces, __________ edges and __________vertices.
Answer:
A triangular pyramid has 4 faces, 6 edges and 4 vertices.
Change the colour.
Page No 370:
Question 40:
Fill in the blanks to make the statements true
A square pyramid has __________ faces, __________ edges and __________ vertices.
Answer:
A square pyramid has 5 faces, 8 edges and 5 vertices.Change the colour
Page No 370:
Question 41:
Fill in the blanks to make the statements true
Out of __________ faces of a triangular prism, __________are rectangles and __________ are triangles.
Answer:
Out of 5 faces of a triangular prism, 3 are rectangles and 2 are triangles.
Change the colour
Page No 370:
Question 42:
Fill in the blanks to make the statements true
The base of a triangular pyramid is a __________.
Answer:
The base of a triangular pyramid is a triangle.
Change the colour
Page No 370:
Question 43:
Fill in the blanks to make the statements true
Out of __________ faces of a square pyramid, __________ are triangles and __________ is/are squares.
Answer:
Out of 5 faces of a square pyramid, 4 are triangles and 1 is/are squares.
Change the colour
Page No 370:
Question 44:
Fill in the blanks to make the statements true
Out of __________ faces of a rectangular pyramid __________ are triangles and base is __________.
Answer:
Out of 5 faces of a rectangular pyramid 4 are triangles and base is rectangle.
Change the colour
Page No 370:
Question 45:
Fill in the blanks to make the statements true
Each of the letters H, N, S and Z has a rotational symmetry of order __________.
Answer:
Each of the letters H, N, S and Z has a rotational symmetry of order 2.
Page No 370:
Question 46:
Fill in the blanks to make the statements true
Order of rotational symmetry of a rectangle is __________.
Answer:
Order of rotational symmetry of a rectangle is 2.
Page No 370:
Question 47:
Fill in the blanks to make the statements true
Order of rotational symmetry of a circle is __________.
Answer:
Order of rotational symmetry of a circle is infinite.
Page No 370:
Question 48:
Fill in the blanks to make the statements true
Each face of a cuboid is a __________.
Answer:
Each face of a cuboid is a rectangle.
Page No 370:
Question 49:
Fill in the blanks to make the statements true
Line of symmetry for an angle is its __________.
Answer:
Line of symmetry for an angle is its bisector.
Page No 370:
Question 50:
Fill in the blanks to make the statements true
A parallelogram has __________ line of symmetry.
Answer:
A parallelogram has no line of symmetry.
Page No 371:
Question 51:
Fill in the blanks to make the statements true
Order of rotational symmetry of
is _________.
Answer:
Order of rotational symmetry of is 8.
Page No 371:
Question 52:
Fill in the blanks to make the statements true
A __________ triangle has no lines of symmetry.
Answer:
A scalene triangle has no lines of symmetry.
Page No 371:
Question 53:
Fill in the blanks to make the statements true
Cuboid is a rectangular_________ .
Answer:
Cuboid is a rectangular prism.
Page No 371:
Question 54:
Fill in the blanks to make the statements true
A sphere has __________vertex, __________edge and __________curved surface.
Answer:
A sphere has 0 vertex, 0 edge and 1 curved surface.
Page No 371:
Question 55:
Fill in the blanks to make the statements true
is a net of a __________.→ Circumference of circle = ______.
Answer:
is a net of a cone → Circumference of circle = 2πr.
Page No 371:
Question 56:
Fill in the blanks to make the statements true
is a net of a __________.
Answer:
is a net of a triangular prism.
Page No 371:
Question 57:
Fill in the blanks to make the statements true
Order of rotational symmetry of
is __________.
Answer:
Order of rotational symmetry of is 1 .
Page No 371:
Question 58:
Fill in the blanks to make the statements true
Identical cubes are stacked in the corner of a room as shown below. The number of cubes that are not visible are _________.
Answer:
Identical cubes are stacked in the corner of a room as shown below. The number of cubes that are not visible are 20 .
Page No 372:
Question 59:
State whether the statement is True or False.
We can draw exactly one triangle whose angles are 70°, 30° and 80°.
Answer:
False.
By using the given angles we can able to draw multiple numbers of triangles.
Page No 372:
Question 60:
State whether the statement is True or False.
The distance between the two parallel lines is the same everywhere.
Answer:
True.
Because parallel lines never intersect each other thus the distance between them is the same everywhere.
Page No 372:
Question 61:
State whether the statement is True or False.
A circle has two lines of symmetry.
Answer:
False.
Circle has infinite lines of symmetry.
Page No 372:
Question 62:
State whether the statement is True or False.
An angle has two lines of symmetry.
Answer:
False.
An angle has one line of symmetry.
Page No 372:
Question 63:
State whether the statement is True or False.
A regular hexagon has six lines of symmetry.
Answer:
True
Since a regular polygon has many lines of symmetry as the number of its sides.
Page No 372:
Question 64:
State whether the statement is True or False.
An isosceles trapezium has one line of symmetry.
Answer:
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.
Page No 372:
Question 65:
State whether the statement is True or False.
A parallelogram has two lines of symmetry.
Answer:
False
Because there is no line of symmetry in a parallelogram.
Page No 372:
Question 66:
State whether the statement is True or False.
Order of rotational symmetry of a rhombus is four.
Answer:
False
Because the order of rotational symmetry of a rhombus is two.
Page No 372:
Question 67:
State whether the statement is True or False.
An equilateral triangle has six lines of symmetry.
Answer:
False
Because there are three lines of symmetry along the three medians of the triangle in an equilateral triangle.
Page No 372:
Question 68:
State whether the statement is True or False.
Order of rotational symmetry of a semi circle is two.
Answer:
False
Because the order of rotational symmetry of a semi-circle is one.
Page No 372:
Question 69:
State whether the statement is True or False.
In oblique sketch of the solid, the measurements are kept proportional.
Answer:
False
In oblique sketch of the solid, the measurements are not kept proportional.
Page No 372:
Question 70:
State whether the statement is True or False.
An isometric sketch does not have proportional length.
Answer:
False
An isometric sketch always has a proportional length.
Page No 372:
Question 71:
State whether the statement is True or False.
A cylinder has no vertex.
Answer:
True
A cylinder has 3 faces, 2 edges but no vertex.
Page No 372:
Question 72:
State whether the statement is True or False.
All the faces, except the base of a square pyramid are triangular.
Answer:
True
A square pyramid has 4 triangular faces and one square base.
Page No 372:
Question 73:
State whether the statement is True or False.
A pyramid has only one vertex.
Answer:
False
A pyramid has at least 4 vertices.
For example: ​In a triangular pyramid, there are 4 vertices.
In a rectangular pyramid, there are 5 vertices.
Page No 372:
Question 74:
State whether the statement is True or False.
A triangular prism has 5 faces, 9 edges and 6 vertices.
Answer:
True
A triangular prism has 5 faces, 9 edges and 6 vertices.
Change the colour
Page No 372:
Question 75:
State whether the statement is True or False.
If the base of a pyramid is a square, it is called a square pyramid.
Answer:
True
Since the name of a pyramid is based on the base of the pyramid. So, if the base of a pyramid is a square, then it is called a square pyramid.
Page No 372:
Question 76:
State whether the statement is True or False.
A rectangular pyramid has 5 rectangular faces.
Answer:
False
A rectangular pyramid has 1 rectangular face and 4 triangular faces.
Page No 372:
Question 77:
State whether the statement is True or False.
Rectangular prism and cuboid refer to the same solid.
Answer:
True
Rectangular prism and cuboid refer to the same solid.
Page No 372:
Question 78:
State whether the statement is True or False.
A tetrahedron has 3 triangular faces and 1 rectangular face.
Answer:
False
A tetrahedron has 4 triangular faces.
Page No 372:
Question 79:
State whether the statement is True or False.
While rectangle is a 2-D figure, cuboid is a 3-D figure.
Answer:
True.
Rectangle has two dimensions i.e., length and width while a cuboid has three dimensions i.e., length, width and height.
Page No 372:
Question 80:
State whether the statement is True or False.
While sphere is a 2-D figure, circle is a 3-D figure.
Answer:
False
Because a sphere is a 3-D figure, a circle is a 2-D figure.
Page No 372:
Question 81:
State whether the statement is True or False.
Two dimensional figures are also called plane figures.
Answer:
True.
A closed two-dimensional or flat figure is called a plane shape.
Page No 372:
Question 82:
State whether the statement is True or False.
A cone is a polyhedron.
Answer:
False
Because a polyhedron is a three-dimensional solid that consists of a collection of polygons. Since cone dose does not have polygonal faces.
Page No 373:
Question 83:
State whether the statement is True or False.
A prism has four bases.
Answer:
False
A prism has only one base.
Page No 373:
Question 84:
State whether the statement is True or False.
The number of lines of symmetry of a regular polygon is equal to the vertices of the polygon.
Answer:
True
The number of lines of symmetry of a regular polygon is equal to the vertices of the polygon.
Page No 373:
Question 85:
State whether the statement is True or False.
The order of rotational symmetry of a figure is 4 and the angle of rotation is 180° only.
Answer:
False
If the order of rotational symmetry of a figure is 4, then the angle of rotation must be 90°.
Page No 373:
Question 86:
State whether the statement is True or False.
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°.
Answer:
True
Page No 373:
Question 87:
State whether the statement is True or False.
Mirror reflection leads to symmetry always.
Answer:
False.
Mirror reflection does not always lead to symmetry.
Page No 373:
Question 88:
State whether the statement is True or False.
Rotation turns an object about a fixed point which is known as centre of rotation.
Answer:
True.
Centre of rotation turns an object about a fixed point.
Page No 373:
Question 89:
State whether the statement is True or False.
Isometric sheet divides the paper into small isosceles triangles made up of dots or lines.
Answer:
False
Isometric sheet divides the paper into small equilateral triangles made up of dots or lines.
Page No 373:
Question 90:
State whether the statement is True or False.
The circle, the square, the rectangle and the triangle are examples of plane figures.
Answer:
True
A closed two-dimensional or flat figure is called a plane shape.
Page No 373:
Question 91:
State whether the statement is True or False.
The solid shapes are of two-dimensional.
Answer:
False
The shapes or figures with three dimensions (length, breadth and height) are known as solids or three-dimensional shapes.
Page No 373:
Question 92:
State whether the statement is True or False.
Triangle with length of sides as 5 cm, 6 cm and 11 cm can be constructed.
Answer:
In a triangle, the sum of any two sides is always greater than or equal to the third side.
5 + 6 = 11
6 + 11 ≥ 5
These measurements do not satisfy the basic condition of a triangle.
Thus, the triangle cannot be constructed.
Page No 373:
Question 93:
Draw the top, side and front views of the solids given below in figures.
Answer:
The top, side and front views of figure 12.21 are as shown below.
The top, side and front views of figure 12.22 are as shown below.
Page No 374:
Question 94:
Draw a solid using the top. side and front views as shown below. [Use Isometric dot paper].
Answer:
ans
Page No 374:
Question 95:
Construct a right-angled triangle whose hypotenuse measures 5 cm and one of the other sides measures 3.2 cm.
Answer:
Steps of construction
Step I: Draw a line AB = 3.2 cm.
Step II: Construct a right angle (90°) at point B, i.e. ∠ABY = 90°
Step III: Now, from point A, cut an arc 5 cm on BY at C.
Step IV: Joint C to A.
Hence, ΔABC is the required triangle, having hypotenuse AC = 5 cm and AB = 32 cm.
Page No 374:
Question 96:
Construct a right-angled isosceles triangle with one side (other than hypotenuse) of length 4.5 cm.
Answer:
Steps of construction
Step I Draw a line AB = 4.5 cm.
Step II Construct a right angle (90°) at point B, i.e. ∠ABY = 90°.
Step III From point B, cut an arc 4.5 cm on BY at C.
Step IV Join C to A.
Hence, ΔABC is the required triangle having AB – AC = 4.5 cm.
Page No 375:
Question 97:
Draw two parallel lines at a distance of 2.2 cm apart.
Answer:
Steps of construction
Step I: Draw a line l and mark a point C outside it.
Step II: Take a point B on line l and join BC.
Step III: Draw a line parallel to line l passing through C.
Step IV: Mark a point D on line m, at a distance of 2.2 cm from C.
Step V Through D draw AD || BC.
Line l is parallel to line m.
Also, AD || BC, AB = DC = 2.2 cm
Page No 375:
Question 98:
Draw an isosceles triangle with each of equal sides of length 3 cm and the angle between them as 45°.
Answer:
Steps of construction
Step I: Draw a rough sketch of triangle with given measures marked on it.
Step II: Draw a line segment AB of length 3 cm.
Step III: Draw an angle of 45° on point B and produce it to ray Y.
Step IV; With B as centre, draw an arc of 3 cm which intersects ray BY at C.
Step V: Join AC.
Thus, ABC is the required isosceles triangle.
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Question 99:
Draw a triangle whose sides are of lengths 4 cm, 5 cm and 7 cm.
Answer:
Let the sides be BC =7 cm, AB = 4 cm and AC = 5 cm.
Steps of construction
Step I: Draw a line BC = 7 cm.
Step II: With centre B and radius 4 cm draw an arc.
Step III: With centre C and radius 5 cm, draw an arc which cuts the previous arc at A.
Step IV: Join AB and AC.
Hence, ΔABC is the required triangle in which AB = 4 cm, BC =7 cm and AC = 5 cm
Page No 375:
Question 100:
Construct an obtuse angled triangle which has a base of 5.5 cm and base angles of 30° and 120°.
Answer:
Steps of construction
Step I: Draw a line segment SC of length 5.5 cm.
Step II: Draw an angle of 120° on point S and produce it to ray Y.
Step III: Draw an angle of 30° on point C and produce it to ray X.
Step IV; Extend BY and CX to intersect at point A.
Hence, ΔABC is the required triangle with BC = 5.5, ∠ABC = 120° and ∠ACB = 30°.
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Question 101:
Construct an equilateral triangle ABC of side 6 cm.
Answer:
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 the previous arc at C.
Step IV: Join A to C and B to C.
Hence, ΔABC is the required triangle.
Page No 375:
Question 102:
By what minimum angle does a regular hexagon rotate so as to coincide with its origional position for the first time?
Answer:
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 the hexagon =
Thus, the minimum angle a regular hexagon rotates so as to coincide with its original position for the first time is 60°.
Page No 375:
Question 103:
In each of the following figures, write the number of lines of symmetry and order of rotational symmetry.
Answer:
| Figure | Number of lines of symmetry | Order of rotational symmetry |
| (a) | 1 | 1 |
| (b) | 1 | 1 |
| (c) | 1 | 1 |
| (d) | 2 | 2 |
| (e) | 1 | 2 |
| (f) | 0 | 1 |
| (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) | 1 | 1 |
| (r) | 0 | 1 |
| (s) | 3 | 13 |
| (t) | 1 | 1 |
| (u) | 10 | 10 |
| (v) | 3 | 3 |
| (w) | 0 | 1 |
Page No 375:
Question 104:
In the figure of a cube,
(i) Which edge is the intersection of faces EFGH and EFBA?
(ii) Which faces intersect at edge FB?
(iii) Which three faces form the vertex A?
(iv) Which vertex is formed by the faces ABCD, ADHE and CDHG?
(v) Give all the edges that are parallel to edge AB.
(vi) Give the edges that are neither parallel nor perpendicular to edge BC.
(vii) Give all the edges that are perpendicular to edge AB.
(viii) Give four vertices that do not all lie in one plane.
Answer:
(i) EF is the intersection of faces EFGH and EFBA.
(ii) Faces EFBA and FBCG intersect at edge FB.
(iii) Faces ABFE, ADHE and ABCD form the vertex A,
(iv) Vertex D is formed by the faces ABCD, CDHG and ADHE.
(v) The edges parallel to edge AB are CD, EF and HG.
(vi) Edges AE, EF, GH and HD are neither parallel nor perpendicular to edge BC.
(vii) Edges AE, BF, AD and BC are perpendicular to edge AB.
(viii) Vertices A, B, G and H do not lie in one plane.
Page No 376:
Question 105:
Draw a net of a cuboid having same breadth and height, but length double the breadth.
Answer:
Required net of a cuboid is
Page No 376:
Question 106:
Draw the nets of the following:
(i) Triangular prism
(ii) Tetrahedron
(iii) Cuboid
Answer:
(i) Net for triangular prism
(ii) Tetrahedron
(iii) Cuboid
Page No 376:
Question 107:
Draw a net of the solid given in the figure
Answer:
The net of the given solid figure is:
Page No 376:
Question 108:
Draw an isometric view of a cuboid 6 cm × 4 cm × 2 cm.
Answer:
Here, l = 6 cm, b = 4 cm and h = 2 cm
Isometric view of a cuboid 6 cm × 4 cm × 2 cm is
Page No 376:
Question 109:
The net given below in figure can be used to make a cube.
(i) Which edge meets AN?
(ii) Which edge meets DE?
Answer:
(i) Edge GH meets edge AN.
Page No 377:
Question 110:
Draw the net of triangular pyramid with base as equilateral triangle of side 3 cm and slant edges 5 cm.
Answer:
The net of a triangular pyramid with the base as an equilateral triangle of side 3 cm and slant edges 5 cm is
Page No 377:
Question 111:
Draw the net of a square pyramid with base as square of side 4 cm and slant edges 6 cm.
Answer:
The net of a square pyramid with the base as the square of side 4 cm and slant edges 6 cm is
Page No 377:
Question 112:
Draw the net of rectangular pyramid with slant edge 6 cm and base as rectangle with length 4 cm and breadth 3 cm.
Answer:
The net of the rectangular pyramid with slant edge of 6 cm and the base is a rectangle with a length of 4 cm and breadth of 3 cm.
Page No 378:
Question 113:
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).
Answer:
(a) Number of cubes in the figure = 6
(b) Number of cubes in the figure = 8
(c) Number of cubes in the figure = 7
(d) Number of cubes in the figure = 8
(e) Number of cubes in the figure = 6
(f) Number of cubes in the figure = 8
(g) Number of cubes in the figure = 6
(h) Number of cubes in the figure = 8
Page No 378:
Question 114:
Draw all lines of symmetry for each of the following figures as given below:
Answer:
(a) Number of lines of symmetry = 1
(b) Number of lines of symmetry = 0
(c) Number of lines of symmetry = 2
Page No 379:
Question 115:
How many faces does figure have?
Answer:
The number of faces in the figure = 16
Page No 379:
Question 116:
Trace each figure. Then draw all lines of symmetry, if it has.
Answer:
(a) Number of lines of symmetry = 2
(b) Number of lines of symmetry = 0
(c) Number of lines of symmetry = 3
Page No 380:
Question 117:
Tell whether each figure has rotational symmetry or not.
Answer:
(a) Yes, the figure has rotational symmetry.
(b) No, the figure does not has rotational symmetry.
(c) Yes, the figure has rotational symmetry.
(d) Yes, the figure has rotational symmetry
(e) Yes, the figure has rotational symmetry
(f) Yes, the figure has rotational symmetry
Page No 380:
Question 118:
Tell whether each figure has rotational symmetry or not.
| (a) | |
(b) | |
| (c) | |
(d) | |
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
Page No 381:
Question 119:
Tell whether each figure has rotational symmetry. Write yes or no.
(a)
(b)
(c)
(d)
Answer:
(a) Yes, the figure has rotational symmetry.
(b) Yes, the figure has rotational symmetry.
(c) No, the figure doesn't have rotational symmetry.
(d) Yes, the figure has rotational symmetry.
Page No 381:
Question 120:
Does the figure have rotational symmetry?
Answer:
The given figure does not show rotational symmetry because one part of the design is not coloured, whereas the other three parts are coloured.
Thus, the design does not show symmetry.
Page No 382:
Question 121:
The flag of Japan is shown below. How many lines of symmetry does the flag have?
Answer:
The given flag has 2 lines of symmetry.
Page No 382:
Question 122:
Which of the figures given below have both line and rotational symmetry?
| (a) | |
(b) | |
| (c) | |
(d) | |
Answer:
Figures in option (a) and (c) has both line and rotational symmetry.
(a) Line symmetry
Rotational symmetry
(b) Line symmetry
Rotational symmetry
Page No 383:
Question 123:
Which of the following figures do not have line symmetry?
| (a) | |
(b) | |
| (c) | |
(d) | |
Answer:
(a) Number of lines of symmetry = 2
(b) Number of lines of symmetry = 0
(c) Number of lines of symmetry = 2
(d) Number of lines of symmetry = 0
Page No 383:
Question 124:
Which capital letters of English alphabet have no line of symmetry?
Answer:
The letters of the English alphabet that have no line of symmetry are F, G, J, L, N, P, Q, R, S and Z.
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