Symmetry | Math Olympiad for Class 5 PDF Download

Q1. A square photo frame is hung on the wall. How many lines of symmetry does it have?
(a) 2
(b) 3
(c) 4
(d) 1
Ans: (c) 4

​A square has four lines of symmetry: one vertical, one horizontal, and two diagonals. This is because folding it along any of these lines makes both halves match perfectly.

Q2. A kite is shaped like a rectangle. How many times does it look the same when rotated 360° around its center?
(a) 2
(b) 4
(c) 3
(d) 1
Ans: (a) 2

 A rectangle has rotational symmetry of order 2. It fits into itself after a 180° rotation and again at 360°, making it look the same twice in one full rotation around its center (where the diagonals meet).

Q3. A circular clock is divided into 12 equal parts for the hours. What is the smallest angle it can be rotated to look the same?
(a) 60°
(b) 45°
(c) 30°
(d) 90°
Ans: (c) 30°

A circle has 360°, and with 12 equal parts, each part is 360° ÷ 12 = 30°. The clock looks the same after every 30° rotation due to its regular division, similar to the rotational symmetry of regular polygons.

Q4. A paper heart is folded in half vertically so both sides match. How many lines of symmetry does it have?
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (a) 1

A heart shape typically has one vertical line of symmetry.

Q5. A hexagonal table mat has 6 equal sides. What is the order of its rotational symmetry?
(a) 4
(b) 6
(c) 5
(d) 8
Ans: (b) 6

A regular hexagon has rotational symmetry of order 6.
 It fits into itself 6 times in a 360° rotation, with the smallest angle of rotation being 360° ÷ 6 = 60°.

Q6. A rectangular mirror is placed vertically. How many lines of symmetry does it have?
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (b) 2

 A rectangle has two lines of symmetry: one vertical and one horizontal. 

Q7. A starfish has 5 equal arms. What is the smallest angle it can be rotated to look the same?
(a) 90°
(b) 60°
(c) 72°
(d) 45°
Ans: (c) 72°

A starfish with 5 equal arms is like a regular pentagon, which has rotational symmetry of order 5. The smallest angle is 360° ÷ 5 = 72°.

Q8. A triangular flag has only one line of symmetry. What type of triangle is it likely to be?
(a) Equilateral
(b) Isosceles
(c) Scalene
(d) Square
Ans: (b) Isosceles

An isosceles triangle has one line of symmetry. An equilateral triangle has 3, and a scalene has none. A square isn’t a triangle, so isosceles fits.

Q9. A cube-shaped box is cut through its center. What shape is the section formed?
(a) Triangle
(b) Rectangle
(c) Square
(d) Circle
Ans: (c) Square

Slicing a cube through its center creates a square section. This is a plane of symmetry dividing the cube into two mirror-image halves, each with a square face.

Q10. A letter ‘H’ is drawn on a card. How many times does it look the same in a 360° rotation?
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (b) 2

The letter ‘H’ has rotational symmetry of order 2. It looks the same after a 180° rotation and again at 360°, fitting into itself twice due to its center of rotation.