Practice Questions: Symmetry | Math Olympiad for Class 5 PDF Download

Q1: What is symmetry?
Ans: Symmetry is when an object or shape looks the same even after you flip, turn, or divide it in special ways.

Symmetry means that an object remains unchanged in appearance after certain transformations like flipping or turning.

Q2: Fill in the blank: "A paper heart folded perfectly in half shows _____ symmetry."
Ans: reflection

When a paper heart is folded in half and both sides look the same, it demonstrates reflection symmetry.

Q3: Identify the type of symmetry in the following statement: "A wheel looks the same at different points as it turns."
Ans: Rotational symmetry

The wheel maintaining the same appearance at different turning points indicates rotational symmetry.

Q4: What is the line of symmetry in a mirror?
Ans: The mirror line

The mirror line is the line of symmetry where the original object and its mirror image are exactly symmetrical.

Q5: Fill in the blank: "ΔA'B'C' is the mirror image of ΔABC. The distance of A' from the mirror is the same as the distance of _____ from the mirror."
Ans: A

Point A' is the mirror image of point A, so their distances from the mirror are equal.

Q6: What happens to the mirror image if a point is farther from the mirror line?
Ans: Its mirror image will be farther from the mirror line.

The farther a point is from the mirror line, the farther its corresponding mirror image will be from the mirror line as well.

Q7: How are the lines AA', BB', and CC' positioned relative to the mirror line?
Ans: They are perpendicular to the mirror line and are bisected by the mirror line.

Lines AA', BB', and CC' meet the mirror line at right angles and are divided into equal parts by the mirror line.

Q8: What do mirrors in a kaleidoscope produce?
Ans: Images of the small pieces of bangles, creating symmetrical designs.

Mirrors in a kaleidoscope reflect the small pieces inside, producing multiple symmetrical patterns.

Q9: Fill in the blank: "To draw a mirror image, we draw perpendiculars from the vertices to the _____ line."
Ans: mirror

Perpendicular lines are drawn from each vertex of the given figure to the mirror line to create the mirror image.

Q10: What is a net of a cube?
Ans: A flat pattern made by joining six identical squares edge to edge that can be folded to form a cube.

A net is a two-dimensional shape that can be folded to create the three-dimensional surface of a cube.

Q11: How many lines of symmetry does a square have?
Ans: Four

A square has four lines of symmetry, dividing it into equal parts in multiple ways.

Q12: What is the order of rotational symmetry for an equilateral triangle?
Ans: 3

An equilateral triangle matches itself three times during a full 360° rotation, giving it rotational symmetry of order 3.

Q13: Fill in the blank: "A rectangle has rotational symmetry of order _____."
Ans: 2

A rectangle fits into its original position twice during a full rotation, so its order of rotational symmetry is 2.

Q14: What is the angle of rotation for a regular hexagon's rotational symmetry?
Ans: 60°

A regular hexagon has rotational symmetry of order 6, so the smallest angle of rotation is 360° ÷ 6 = 60°.

Q15: Why do some figures have only rotational symmetry but no linear symmetry?
Ans: Because they can only match themselves by rotating but do not have lines that divide them into mirror images.

Figures like the letters N, S, and Z can be rotated to match their original shape but lack lines of symmetry that create mirror images.