# Free Symmetry Subjective Test 02 Practice Test - 6th grade

Which of the following represents a symmetrical figure? [1 MARK] #### SOLUTION

Solution :

If a figure can be folded or divided in such a way that the two halves match exactly, such a figure is called a symmetrical figure.
In the given options, the image of the butterfly is the only one which can be divided into two symmetrical halves.

We often see these types of signals on traffic sign boards. State whether they are mirror images of each other or not. [2 MARKS] #### SOLUTION

Solution :

Yes/No: 1 Mark
Reason: 1 Mark

Yes, they are mirror images of each other. The mirror image is the image formed by reflection of an object on the mirror. If we try to overlap one arrow over the another then they will completely fit on one another.

What is the name of the given triangle? How many line(s) of symmetry is/are possible for the given figure? [2 MARKS] #### SOLUTION

Solution :

Name: 1 Mark
Correct answer with diagram: 1 Mark

The given figure is an isosceles triangle where two sides are equal. We can have one line of symmetry for this triangle. It is shown below. A rectangular cricket field is to be divided into two parts. How can it be divided in order to get two more symmetrical rectangular fields? Show it with a diagram. [3 MARKS]

#### SOLUTION

Solution :

How: 2 Marks
Diagram: 1 Mark

There are two ways in which we can divide a rectangular field into two similar fields. The lines should pass through the midpoint of the two sides which are opposite to each other. For rectangles, we have 2 lines of symmetry. (a) What is required for a kaleidoscope to produce images?
(b) Do the images so produced have any line of symmetry? If yes, what determines the number of lines of symmetry?  [3 MARKS]

#### SOLUTION

Solution : (a) 1 Mark
(b) 2 Marks

(a) A kaleidoscope uses mirrors to produce images. (b) Yes, the images formed can have several lines of symmetry. The number of lines of symmetry is determined by the angle between the mirrors.

How many lines of symmetry are possible for an octagon? Show it with a diagram. [3 MARKS]

#### SOLUTION

Solution :

Answer with Concept: 2 Marks
Diagram: 1 Mark

Any regular octagon has 8 lines of symmetry: 4 through opposite vertices and 4 through midpoints of parallel sides. The dotted lines show that the half figure is a mirror image of the other half. (a) A drop of ink fell on one edge of a rectangular paper. After that, the paper was folded 2 times. How many such symmetrical ink droplet will you find?

(b) Copy the diagram given  below and complete each shape to be symmetric about the mirror line:  [4 MARKS] #### SOLUTION

Solution :

Each point: 2 Marks

(a) The paper will get 4 such symmetrical droplets. (b) The image about the mirror line is shown below: (a) A diagram has 5 lines of symmetry. Draw all the lines of symmetry and then divide the figure into 10 parts. Given here is a part of the diagram. Complete the diagram. [4 MARKS] (b) How many lines of symmetry does a polygon with its adjacent sides equal and perpendicular have?

#### SOLUTION

Solution :

Each option: 2 Marks

(a) The asked diagram is a pentagon. (b) A polygon with adjacent sides equal and perpendicular is a square. A square has 4 lines of symmetry. (a) Identify multiple lines of symmetry, if any, in the following figure:  [4 MARKS] (b) Copy the diagram and make a symmetric shape about the mirror line. #### SOLUTION

Solution : Visualisation: 1 Mark each
Diagram: 1 Mark each

(a) The following figure will have 6 distinct lines which will cut the figure into identical halves. Hence, lines of symmetry are 6.

Lines of symmetry (b)  The completed shape symmetric about the mirror line is shown below: (a) In the figure below, can u determine if the pattern is symmetrical and if symmetrical how many lines of symmetry are possible for the following figure? (b) Name a geometrical figure that has seven lines of symmetry. Draw a diagram showing the lines of symmetry.

#### SOLUTION

Solution : (a)  2 Marks
(b)  2 Marks

(a) In the given figure, one line of symmetry is possible as depicted in the image below. By folding the figure about this line it will overlap completely. (b) Any line which divides a diagram into two equal halves is called a line of symmetry. This line of symmetry divides the figure into two identical halves. If a random diagram has 7 such lines, it will have 7 lines of symmetry.

The most basic figure that would have 7 lines of symmetry can be a regular heptagon with all 7 sides equal. 