Chapter 12: Practical Geometry Symmetry and Visualising Solid Shapes

Ans:  Option (b) is the correct answer.

A triangle is possible, when the sum of two sides is greater than the third side. Use the hit and trial method and check the all options:

For option (a),

$1.8{\text{cm}} + 2.6{\text{cm}} = 4.4{\text{cm}}$, which is equal to third side

For option (b),

$2{\text{cm}} + 3{\text{cm}} = 5{\text{cm}}$, which is greater than third side

For option (c),

$2.4{\text{cm}} + 2.4{\text{cm}} = 4.8{\text{cm}}$, which is less than third side

For option (d),

$3.2{\text{cm}} + 2.3{\text{cm}} = 5.5{\text{cm}}$, which is equal to the third side.

Thus, only option (b) satisfies the condition. Therefore, option (b) is right.

Ans: Option (a) is the correct answer.

A triangle is possible, when the sum of all interior angles is equal to $180^{\circ}$. Use the hit and trial method and check the all options:

For option (a),

${110^\circ } + {40^\circ } = {150^\circ }$ and third angle is ${30^\circ }$

For option (b),

${70^\circ } + {115^\circ } = {185^\circ }$, is greater than ${180^\circ }$

For option (c),

${135^\circ } + {45^\circ } = {180^\circ }$, third angle is ${0^\circ }$

For option (d),

${90^\circ } + {90^\circ } = {180^\circ }$, third angle is ${0^\circ }$

Thus, only option (a) satisfies the condition.

Therefore, option (a) is the correct answer.

Solution coming soon.

Ans: Option (b) is the correct answer.

Symmetrical line is the line which divides a figure into two equal parts.

Here, the figure has only a $3$ line of symmetry. Therefore, option (b) is the correct answer.

Ans: Option (c) is the correct answer.

In a complete turn of ${360^\circ }$, the number of times the figure coincides with its original position is called its order of rotational symmetry. Here, the order of rotational symmetry is $6$. Therefore, option (c) is the correct answer.

Ans: Option (b) is the correct answer.

In a complete turn of ${360^\circ }$, the number of times the figure coincides with its original position is called its order of rotational symmetry. Here, the order of rotational symmetry is $2$. Therefore, option (b) is the correct answer.

Ans: Option (b) is the correct answer.

A pyramid is a three dimensional polyhedron shaped structure with only one polygonal base and has triangular sides. A prism is a three dimensional polyhedron characterized by two bases which are polygonal in shape and rectangular sides perpendicular to the base. Here, the given figure contains rectangle base and triangle sides. Thus, the given figure is the combination of a rectangle and triangle called a rectangular pyramid. Therefore, option (b) is the correct answer.

Ans: Option (c) is the correct answer.

A pyramid is a three dimensional polyhedron shaped structure with only one polygonal base and has triangular sides. A prism is a three dimensional polyhedron characterized by two bases which are polygonal in shape and rectangular sides perpendicular to the base. Here, the given figure contains parallelogram faces and triangle sides. Therefore, the given figure is the combination of parallelogram and triangle called triangular prism. 

Ans: Option (d) is the correct answer.

The all faces of a pyramid are triangular except base as it depends on the type of pyramid. Therefore, option (d) is the correct answer.

Ans: Option (c) is the correct answer.

Vertex is defined as the common endpoint of two or more rays or line segments. And it typically means a corner or a point where lines meet. A pyramid is a three dimensional polyhedron shaped structure with only one polygonal base and has triangular sides and it has five vertices. A cube is a regular hexahedron and it has eight vertices. A cylinder has no vertex, since its faces never meet. A solid that has only one vertex is called a cone.

Therefore, option (c) is the correct answer.