Chapter 12: Practical Geometry Symmetry and Visualising Solid Shapes

Q21Written answer

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

(a) ${\mathbf{AB = 4cm,}}\,\,{\mathbf{BC = 8cm}}$ and ${\mathbf{CA = 2cm}}$

(b) $BC=5.2 cm$ $\angle B = {90}^{\circ}$ and $\angle C = {110}^{\circ}$

(c) $XY=5 cm$ $\angle X = {45}^{\circ}$ and $\angle Y = {60}^{\circ}$

(d) An isosceles triangle with the length of each equal side ${\mathbf{6}}{\mathbf{.2cm}}$.

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Ans: Option (c) is the correct answer.

A triangle Is possible if:

(i) Sum of any two sides must be greater than the third side of the triangle.

(ii) Sum of all angles must be equal to $180^{\circ}$.

So, options (a) and (b) triangles are not possible because of the above points (i) and (ii) respectively.

In option (d) we can draw more than one isosceles triangle with side length $6.2$ $\mathrm{cm}$. So, triangles are not unique.

Thus, a unique triangle can be drawn only in option (c).

Q22Written answer

Which of the following has a line of symmetry?

(a)

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Ans: Figure (c) has a line of symmetry.

A figure has line symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide with each other.

Therefore, figure (c) has a line of symmetry.

Q23Written answer

Which of the following are reflections of each other?

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Ans: Figures in (a) are reflections of each other.

Mirror reflection leads to symmetry, under which the left-right orientation has to be taken care of. Therefore, option (a) is the correct answer.

Q24Written answer

Which of these nets is a net of a cube?

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Ans: Option (b) is the correct answer.

Figure (b) is a net of cube.

Q25Written answer

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

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Ans: Option (b) is the correct answer.

Figure (c) is a net of a cylinder.

Q26Written answer

Which of the following letters of English alphabets have more than ${\mathbf{2}}$ lines of symmetry?

(a) Z

(b) O

(c) E

(d) H

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Ans: Option (b) is the correct answer.

Figure (b) ‘O’ has more than $2$ lines of symmetry.

Q27Written answer

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 ${\mathbf{3}}$ pieces in 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?

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Ans: Option (a) is the correct answer.

On opening the piece of paper shapes, we get a shape like figure (a).

Q28Written answer

Which of the following ${\mathbf{3}}$-dimensional figures has the top, side and front as triangles?

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Ans: Figure (c) has a top, side and a front as triangles.

Therefore, option (c) is the correct answer.

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

Q29Written answer

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

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Ans: The isosceles right triangle is given by,

From the figure, it is clear that it has one line of symmetry. Therefore, In an isosceles right triangle, the number of lines of symmetry is one.

Q30Written answer

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

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Ans: Rhombus is a figure that has two lines of symmetry and has a rotational symmetry of order two.

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