Test: Symmetry - 1 - Class 6 MCQ

A regular pentagon has 5 lines of symmetry, one for each vertex and the midpoint of the opposite side.

The shape that will look the same after being rotated by 180 degrees is an equilateral triangle. This is because the equilateral triangle has rotational symmetry of order 3, meaning it looks the same when rotated by 120°, 180°, or 240°.

For example: If you rotate an equilateral triangle by 180 degrees, it will still look identical, as all its sides and angles are equal.

An equilateral triangle has 3 lines of symmetry, each passing through a vertex and the midpoint of the opposite side.

A square has rotational symmetry at 90 degrees, which means it looks the same after a 90-degree rotation.

A scalene triangle does not have rotational symmetry. A scalene triangle has all sides and angles of different lengths and degrees, so it cannot be rotated around its center and map onto itself unless it is rotated by 360°, which would bring it back to the original position, but there are no smaller rotational angles that would map it onto itself.

Explanation of the other figures:

• A: Equilateral Triangle – Has rotational symmetry at 120°, 240°, and 360°.
• B: Rectangle – Has rotational symmetry at 180° and 360°.
• C: Circle – Has infinite rotational symmetry, as it looks the same at any angle of rotation.

So, the correct answer is D: Scalene Triangle.

When a circle is folded along any diameter, the two halves overlap perfectly. This is because the diameter divides the circle into two congruent halves, and when folded along this line, the two halves align perfectly with each other.

The correct answer is A: The two halves overlap perfectly.

The shape that has no lines of symmetry is a scalene triangle. A scalene triangle has no equal sides or angles, so it does not have any lines of symmetry.

Explanation of the other shapes:

• B: Square – A square has 4 lines of symmetry (2 diagonals and 2 midlines).
• C: Rectangle – A rectangle has 2 lines of symmetry (the two midlines).
• D: Regular Pentagon – A regular pentagon has 5 lines of symmetry.

So, the correct answer is A: Scalene Triangle.

A regular hexagon has 6 lines of symmetry. Each line of symmetry passes through a vertex and the midpoint of the opposite side, with one line through each vertex.

The correct answer is D: 6.

The order of rotational symmetry of a regular pentagon is 5. This means that you can rotate a regular pentagon by multiples of 360°/5 = 72 (i.e., 72°, 144°, 216°, 288°, and 360°) and it will map onto itself at each of these rotations.

The correct answer is C: 5.

A rhombus has 2 lines of symmetry. These lines of symmetry pass through the diagonals, which bisect each other at right angles and divide the rhombus into two congruent parts.

The correct answer is (c) 2.