A line that divides a figure into two parts that exactly overlap when folded along that line is called a line of ____.
Why: A line of symmetry creates mirror halves.
If one half of a figure covers the other half completely when folded along a line, these halves are called mirror halves.
Why: Mirror halves perfectly overlap when folded.
Which of the following letters has a vertical line of symmetry?
Why: The letter 'A' can be folded vertically into two identical halves.
A square has exactly two lines of symmetry.
Why: A square has four lines of symmetry.
The fixed point about which an object is rotated in rotational symmetry is called the centre of ____.
Why: The fixed point for rotation is the centre of rotation.
Which of the following figures has no line of symmetry?
- Equilateral triangle
- Isosceles triangle
- Scalene triangle (correct)
- Rectangle
Why: A scalene triangle has no equal sides or angles, thus no line of symmetry.
An angle through which a figure can be rotated to look exactly the same is called an angle of rotational ____.
Why: This angle is known as the angle of rotational symmetry.
A circle has an infinite number of lines of symmetry.
Why: Any line passing through the center of a circle is a line of symmetry.
Which of these shapes has only one line of symmetry?
- Square
- Rectangle
- Isosceles triangle (correct)
- Circle
Why: An isosceles triangle has one line of symmetry that bisects its unique angle.
A figure has rotational symmetry if it looks exactly the same after being rotated by an angle strictly between 0 and ____ degrees.
Why: Rotational symmetry occurs for angles between 0 and 360 degrees.
Which of the following letters has both horizontal and vertical lines of symmetry?
Why: The letter 'H' can be folded both horizontally and vertically into identical halves.
A figure that looks exactly the same when rotated by an angle about a fixed point is said to have rotational symmetry.
Why: This is the definition of rotational symmetry.
A regular hexagon has how many lines of symmetry?
Why: A regular hexagon has 6 lines of symmetry.
A figure can have multiple lines of symmetry.
Why: Many figures, like squares or circles, have multiple lines of symmetry.
The repetition of parts in a definite pattern in a figure is called ____.
Why: Symmetry describes patterns and repetitions in figures.
Which of the following figures has exactly two lines of symmetry?
- Equilateral triangle
- Rhombus (correct)
- Regular pentagon
- Scalene triangle
Why: A rhombus has two lines of symmetry along its diagonals.
Match the shapes with their number of lines of symmetry.
Why: Each shape has a specific number of lines of symmetry.
What is the order of rotational symmetry for a square?
Why: A square looks the same after 4 rotations within 360 degrees.
Arrange the following shapes in increasing order of their number of lines of symmetry: Rectangle, Equilateral Triangle, Square, Circle.
Why: The order is Rectangle (2), Equilateral Triangle (3), Square (4), Circle (Infinite).
Observe the given figure. How many lines of symmetry does it have?
Why: A cross shape formed by squares typically has 4 lines of symmetry.
Which of the following statements is true regarding symmetry?
- All symmetrical figures have rotational symmetry.
- A figure can have rotational symmetry but no line of symmetry. (correct)
- All figures with a line of symmetry also have rotational symmetry.
- A figure can only have one angle of rotational symmetry.
Why: Some figures, like a pinwheel, have rotational but no line symmetry.
Match the letters with their number of lines of symmetry.
Why: Each letter has a distinct number of lines of symmetry.
What is the smallest angle of rotational symmetry for a regular pentagon?
Why: A regular pentagon has 5 equal sides, so 360/5 = 72 degrees.
Identify the figure that has both line symmetry and rotational symmetry.
- Letter 'P'
- A regular hexagon (correct)
- A human hand
- A cloud
Why: A regular hexagon has both 6 lines of symmetry and rotational symmetry of order 6.
Which of the following figures has rotational symmetry but no line of symmetry?
- Figure A (Square)
- Figure B (Isosceles Triangle)
- Figure C (Pinwheel) (correct)
- Figure D (Rectangle)
Why: A pinwheel is a classic example of rotational symmetry without line symmetry.
Match the shapes with their order of rotational symmetry.
Why: The order of rotational symmetry for regular polygons equals their number of sides.
Arrange the following angles in increasing order of their value: Smallest angle of rotational symmetry for a square, Smallest angle of rotational symmetry for an equilateral triangle, Smallest angle of rotational symmetry for a regular hexagon.
Why: Hexagon (60°), Square (90°), Equilateral Triangle (120°).
A figure is shown with a dotted line. Does this dotted line represent a line of symmetry?
- Yes, because it divides the figure into two parts.
- No, because the two parts do not overlap exactly when folded. (correct)
- Yes, because it passes through the center of the figure.
- It is impossible to tell without folding.
Why: For a line to be a line of symmetry, the halves must perfectly overlap.
Which of the following letters has only a horizontal line of symmetry?
Why: The letter 'B' can be folded horizontally into two identical halves.
Consider a regular octagon. How many lines of symmetry does it have?
Why: A regular octagon has 8 sides, so it has 8 lines of symmetry.
A figure has rotational symmetry of order 5. What is the smallest angle (in degrees) by which it can be rotated to look exactly the same?
Why: Order 5 means 5 rotations in 360 degrees, so 360/5 = 72 degrees.
Assertion (A): A rectangle has rotational symmetry of order 2. Reason (R): A rectangle looks the same after a rotation of 180 degrees.
Why: A rectangle has order 2 rotational symmetry because it looks the same after 180° rotation.
A design is made of four identical heart shapes arranged around a central point. If the design has rotational symmetry of order 4, what is the smallest angle (in degrees) of rotation?
Why: Order 4 rotational symmetry means the smallest angle is 360/4 = 90 degrees.
A figure has 6 lines of symmetry. What is the order of its rotational symmetry?
Why: For regular polygons, the number of lines of symmetry equals the order of rotational symmetry.
Observe the given figure of a star. How many lines of symmetry does it have?
Why: A regular 5-pointed star has 5 lines of symmetry, each passing through a point and the opposite indentation.
Assertion (A): A figure can have multiple angles of symmetry. Reason (R): A square has angles of symmetry at 90 degrees, 180 degrees, and 270 degrees.
Why: A square's multiple angles of symmetry demonstrate that figures can have more than one.
A clock face has rotational symmetry. Ignoring the hands, if you rotate the clock face, it looks the same at certain intervals. What is the smallest positive angle (in degrees) of rotational symmetry for a standard 12-hour clock face?
Why: A 12-hour clock face has 12 distinct positions, so 360/12 = 30 degrees.
A company logo is designed using a regular hexagon. The logo needs to be printed on various merchandise. If the logo is rotated by 240 degrees, will it look exactly the same as the original?
- Yes, because a regular hexagon has rotational symmetry. (correct)
- No, because 240 degrees is not a multiple of 60 degrees.
- Yes, but only if the hexagon is also symmetrical along its diagonals.
- No, it will only look the same at 60, 120, 180, and 300 degrees.
Why: A regular hexagon's smallest angle of rotation is 60°, and 240° is a multiple of 60°.
A figure has both line symmetry and rotational symmetry. If it has 4 lines of symmetry, what is the smallest angle (in degrees) of its rotational symmetry?
Why: 4 lines of symmetry implies a regular polygon with 4 sides (square), so 360/4 = 90 degrees.
Consider the given figure, which is a combination of two identical equilateral triangles joined at a vertex. How many lines of symmetry does this combined figure have?
Why: The combined figure has one line of symmetry passing through the common vertex and the midpoints of the opposite bases.
