Test:Symmetry - 2 - Class 6 MCQ

When you rotate a square by 90 degrees, it looks the same. This is because a square has rotational symmetry of 90°, meaning it can be rotated by 90°, 180°, 270°, or 360° and still look identical.

The correct answer is A: It looks the same.

A regular octagon has 8 lines of symmetry. Each line of symmetry passes through either a vertex and the midpoint of the opposite side, or the midpoints of opposite sides.

The correct answer is C: 8.

The shape that has only one line of symmetry is an isosceles triangle. An isosceles triangle has two equal sides and one line of symmetry that runs from the vertex opposite the base to the midpoint of the base.

Explanation of the other shapes:

• A: Square – A square has 4 lines of symmetry.
• B: Rectangle – A rectangle has 2 lines of symmetry.
• C: Circle – A circle has infinite lines of symmetry.

The correct answer is D: Isosceles Triangle.

The smallest angle of rotation that maps a regular hexagon onto itself is 60°.

A regular hexagon has rotational symmetry of order 6, meaning it can be rotated by multiples of 60° (i.e., 60°, 120°, 180°, 240°, 300°, and 360°) and still map onto itself.

So, the correct answer is B: 60°.

When you fold a kite shape along its line of symmetry, the two halves overlap perfectly. A kite has one line of symmetry, which divides it into two congruent triangles. 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 rotational symmetry but no line of symmetry is a parallelogram (excluding rectangles and squares). A parallelogram has rotational symmetry of 180°, meaning it can be rotated by 180° and still map onto itself. However, it does not have any lines of symmetry unless it is a special case (like a rectangle or rhombus).

Explanation of the other shapes:

• A: Circle – A circle has infinite lines of symmetry and rotational symmetry.
• B: Scalene Triangle – A scalene triangle has no lines of symmetry and no rotational symmetry other than at 360°.
• C: Rectangle – A rectangle has both rotational symmetry (180°) and two lines of symmetry.

The correct answer is D: Parallelogram.

When you rotate a regular pentagon by 72 degrees, it looks the same. A regular pentagon has rotational symmetry of 72°, meaning it can be rotated by multiples of 72° (72°, 144°, 216°, 288°, and 360°) and still look identical.

The correct answer is A: It looks the same.

In a regular polygon with n sides, the number of lines of symmetry is n. This is because a regular polygon has as many lines of symmetry as it has sides, with each line of symmetry passing through a vertex and the midpoint of the opposite side (or through the midpoints of opposite sides in some cases).

The correct answer is (c) n.

A square has 4 lines of symmetry. These include:

• 2 diagonals (from vertex to opposite vertex)
• 2 lines of symmetry through the midpoints of opposite sides.

The correct answer is C: 4.

The figure that has infinitely many lines of symmetry is a circle. A circle has rotational symmetry and any line passing through its center is a line of symmetry, meaning there are infinitely many lines of symmetry.

The correct answer is (c) Circle.