D1 Symmetry

What is the order of turn symmetry for the given figure?

• 2

• 5

• 4

• 3

Answer explanation

The question asks for the order of turn symmetry for the given figure. To find the correct answer, we need to analyze the options. Option 2, 4, and 5 are incorrect as they do not match the given figure. Option 3 is the correct choice as it represents the correct order of turn symmetry. Therefore, the answer is 3.

How many axes of rotation are there in a regular tetrahedron?

• 3

• 4

• 7

• 9

Answer explanation

A regular tetrahedron has 7 axes of rotation. The given question asks about the number of axes of rotation in a regular tetrahedron. The correct answer is 7. Therefore, the answer explanation highlights that a regular tetrahedron has 7 axes of rotation.

The total number of axis of rotation in a cube is

• 6

• 8

• 10

• 13

Answer explanation

The question asks about the total number of axis of rotation in a cube. The correct answer is 13. A cube has 12 edges, and each edge can be considered as an axis of rotation. Additionally, the cube has a central axis passing through its center. Therefore, the total number of axis of rotation in a cube is 13.

Which of the following statements is NOT TRUE?

• The turn symmetry of a regular hexagonal pyramid is 6.

• Circum-centre of a right triangle will be on the hypotenuse.

• The ortho-centre is a point of intersection of the medians.

• An altitude of a triangle is a perpendicular line segment from a vertex of a triangle to its opposite sides.

Answer explanation

The ortho-centre is not a point of intersection of the medians. The ortho-centre is the point of intersection of the altitudes of a triangle. The altitudes are perpendicular lines drawn from each vertex of the triangle to its opposite side. Therefore, the statement 'The ortho-centre is a point of intersection of the medians' is not true.

What is the number of planes of symmetry in a regular pentagon-based prism?

• 4

• 5

• 6

• 7

Answer explanation

A regular pentagon-based prism has 6 planes of symmetry. These planes divide the prism into identical halves. The correct choice is 6, as it matches the number of planes of symmetry in the prism. The question asks for the number of planes of symmetry, not the number of sides or vertices. Therefore, the answer is 6.

What is the order of turn symmetry for a regular octagon?

• 7

• 8

• 9

• 10

Answer explanation

The order of turn symmetry for a regular octagon is 8. This means that the octagon can be rotated 8 times to coincide with its original position. The correct choice is '8'. The question asks for the order of turn symmetry, not the number of sides or angles. Therefore, options 7, 9, and 10 are incorrect. The answer explanation highlights the correct choice without mentioning the option number. The question is about the order of turn symmetry, not the query.

The number of planes of symmetry in a regular hexagon-based prism is

• 0

• 5

• 6

• 7

Answer explanation

The number of planes of symmetry in a regular hexagon-based prism is 7. This means that there are 7 different ways to rotate the prism so that it looks the same from multiple angles. The correct choice is 7, as stated in the answer. The prism has 7 planes of symmetry, which is the highest number among the given options. The question asks for the number of planes of symmetry, not the number of sides or vertices. Therefore, the answer is 7.

How many lines of symmetry does a square have?

• 2

• 3

• 4

• 8

Answer explanation

A square has 4 lines of symmetry. This means that it can be divided into 4 equal parts that can be folded or rotated to match each other. The correct choice is 4, as it represents the number of lines of symmetry in a square.

The number of the axes of rotation of a rectangular prism that is not a cube is

• 2

• 3

• 5

• 8

Answer explanation

The question asks about the number of axes of rotation for a rectangular prism that is not a cube. The correct answer is 3. A rectangular prism has three axes of rotation: one along the length, one along the width, and one along the height. This allows the prism to be rotated in three different directions. The other options, 2, 5, and 8, are incorrect as they do not represent the correct number of axes of rotation for a rectangular prism.

Which of the following shapes does not have reflectional symmetry?

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