Free Symmetry 03 Practice Test - 7th grade
Rotational symmetry and radial symmetry have same meanings. Is the statement True or False?
Solution : A
Rotational symmetry in biological sense is known as radial symmetry. They are things with same meaning but different names.
It is just like mirror/reflection symmetry.
If the order of symmetry of the first image is ‘A’ and the second image is ‘B’. Find the value of A + B.
A wind mill has order 3 rotational symmetry. Did you notice that after the third rotation, it looks exactly as it looked at the start? We got total of three instances where the wind mill looked exactly like as the start.
The key-point is the final position of any object, after 360° rotation will always look like the initial object. So, every object will have rotational symmetry of order 1.
Let us move on to the question now.
In 1, for 360° rotation, we have two instances where it looks like the starting position. That is after 180° and after 360°. So, the order is 2 which will be the value of ‘A’.
But fig. 2 has order 1 because it only repeats itself after 360° rotation. So, B = 1.
That means A + B = 2 + 1 = 3
Find the number of letters(upper case) in English alphabet which have rotational symmetry. Answer in terms of a number.
As it turns out, any figure which has point symmetry exhibits rotational symmetry around that point of symmetry. So, letters which have point symmetry will have rotational symmetry for sure. So, the letters that will fall under this category are:
H, I, N, O, S, X, Z
But we can’t be sure that these are the only letters which have rotational symmetry. A letter with rotational symmetry may not have point symmetry. Fortunately, there are no alphabets like that. So, 7 is the answer.
Which of the following cannot be the angle of rotational symmetry of a regular polygon?
Solution : C
The angle of rotation of a 'n' sided regular polygon is given by 360∘n.
We know that minimum value of n is 3 as the minimum number of sides required to make a polygon is 3.
∴ The angle of rotational symmetry of a regular polygon will always be less than or equal to 120∘.
How many angles of rotation a regular polygon will have if it has ‘n’ sides?
Solution : B
Angles of rotation of a regular polygon with ‘n’ sides = Y = n – 1
This is because the last rotation, i.e. 360∘ is not counted as an angle of rotation. If it was counted as an angle of rotation, every object would have an angle of rotation.
So, angles of rotation for a square are 90∘, 180∘ and 270∘. It’s only 3, not 4.
The lines of symmetry of a regular polygon with n sides divide the polygon into __ triangles.
Solution : C
The 3 lines of symmetry of an equilateral triangle (a regular polygon with 3 sides) divide it into 6 triangles.
The 4 lines of symmetry of a square (a regular polygon with 4 sides) divide it into 8 triangles.
Hence, a regular polygon with n sides will be divided into 2n triangles when all its lines of symmetry are drawn.
Which of the figures given below are symmetric?
(Each figure has given a number from 1 to 4. Select the corresponding number.)
Solution : A and D
Shapes or figures which have evenly balanced proportions are called symmetric figures. In other words, if on folding a figure, one half exactly aligns or superimposes the other, then the figure is said to be symmetric and the line which divides the figure into two equal halves is called a line of symmetry.
Figures 1 and 4 are symmetric with respect to the line of symmetry shown below:
<Two friends arguing>
Arjun: If a figure can be folded along any line such that one half superimposes the other, it is known as symmetric figure.
Shubh: If you can find a line in the figure which divides it in identical parts, then the figure is always symmetric.
Solution : B
If a figure can be folded along any line such that one half superimposes or aligns exactly with the other, it is known as symmetric figure.
For example: If you take a square and fold it across the line shown, part 1 exactly overlaps part 2. So, square is a symmetric figure.
On the other hand, in a parallelogram, the diagonal divides it into two congruent triangles (can be proven using SSS congruence condition), i.e. into two equal parts. But those parts don’t superimpose each other when folded across diagonal (as shown in the figure). So, parallelogram is not symmetric.
Hence, Arjun is right and Shubh is wrong.
Match the figures to their number of lines of symmetry.
Solution : C
A regular hexagon has six, a the regular pentagon has five and a square has four lines of symmetry. A regular polygon of n sides has n lines of symmetry.
A rectangle has only two lines of symmetry as shown below.
Considering the types of triangles on the basis of sides, how many lines of symmetry can a triangle possibly have?
Solution : A, B, and D
Triangles can be categorized into three types based on sides:
- Scalene Triangles: Have no lines of symmetry as all sides are unequal.
- Isosceles Triangles: Have 1 line of symmetry as only two of the sides are equal.
- Equilateral Triangles: Have 3 lines of symmetry as all sides are equal.
The same is shown in the figure below: