# Free Symmetry Subjective Test 01 Practice Test - 6th grade

Define line of symmetry. [1 MARK]

#### SOLUTION

Solution :

The line of symmetry is an imaginary line, when we fold the figure along the dotted line of symmetry, the figure is exactly divided into two identical halves.

(a) State whether L is the line of symmetry or not assuming that the thickness of the pizza is negligible? [2 MARKS] (b)
How many lines of symmetry are possible for this figure? #### SOLUTION

Solution :

Each option: 1 Mark

(a) Yes, L is the line of symmetry as it divides the pizza into two identical parts.

(b)
We can have only one line of symmetry for this figure. How many lines of symmetry are possible? [2 MARKS]
a. For a circle
b. For a scalene triangle

#### SOLUTION

Solution : Each option: 1 Mark

a. A circle can have infinite lines of symmetry.
b. Scalene triangles have no lines of symmetry.

In how many ways can the given figure be divided into two equal parts? how? [3 MARKS] #### SOLUTION

Solution :

Reason: 1 Mark
Diagram: 1 Mark

This figure can be divided into two equal parts in 4 ways. It has 4 lines of symmetry. How many lines of symmetry are possible for an equilateral triangle. Explain with a proper diagram? [3 MARKS]

#### SOLUTION

Solution :

Diagram: 1 Mark
Explanation: 1 Mark

For an equilateral triangle, we have 3 lines of symmetry. It can be divided into two equal parts in 3 ways. Draw a polygon with six lines of symmetry. What is it called? [3 MARKS]

#### SOLUTION

Solution :

Diagram: 1 Mark
Labelling: 1 Mark
Naming: 1 Mark

A polygon having six lines of symmetry is a regular hexagon. A milkman wants to park his bike at some point Q and deliver the milk to two different houses A and B. Where should he park the bike so that his walking distance AQ + BQ will be minimum? [4 MARKS]

#### SOLUTION

Solution :

Visualisation of question: 1 Mark
Steps: 1 Mark
Concept: 1 Mark

Here, we can use reflection symmetry in order to find the minimum distance. Let's take the mirror image of house A as A'. So, for minimum distance Q must lie in centre e.g. Q must be the line of symmetry for a mirror image of house A and house B and height of A' and A are equal. So, the milkman should park his bike at the centre point of the distance between houses A and B. (a) A piece of paper is folded as shown below. How many symmetrical figures are possible after unfolding figure no. 3? [2 MARKS] (b)
How many lines of symmetry are possible for this figure? [2 MARKS] #### SOLUTION

Solution :

a) 2 Marks
b) 2 Marks

(a) The piece of paper is folded 2 times.  So, when we open that piece of paper, we get 4 symmetrical squares. (b)
For this figure, we can have 6 lines of symmetry. Complete the following diagrams by drawing the mirror images.  [4 MARKS]

(i) (ii) (iii) (iv) #### SOLUTION

Solution :

Completed Figures: 1 Mark each

(i) (ii) (iii) (iv) What letters of the English alphabet have reflection symmetry about:
a) A Vertical mirror
b) A Horizontal mirror  [4 MARKS]

#### SOLUTION

Solution :

Each Option: 2 Marks

a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y Horizontal mirror - B, C, D, E, H, I, O and X 