Olympiad Test: Symmetry - Free MCQ with solutions CTET Mathematics & Pedagogy

• A has one line of symmetry (vertical).
• B has one line of symmetry (vertical).
• Q has no line of symmetry. Although it has a circular shape, it is asymmetric due to the tail of the letter.
• O has infinite lines of symmetry (both vertical and horizontal).

Thus, the correct answer is Option C: Q.

• A has one line of symmetry (vertical).
• O has infinite lines of symmetry. It has both vertical and horizontal symmetry, and also diagonal symmetries, making it the letter with many lines of symmetry.
• Q has no line of symmetry. Although it has a circular shape, it is asymmetric due to the tail of the letter.
• B has one line of symmetry (vertical).

Thus, the correct answer is Option B: O.

A rectangle has two lines of symmetry:

• One vertical line of symmetry that divides the rectangle into two equal parts.
• One horizontal line of symmetry that divides the rectangle into two equal parts.

Thus, the correct answer is Option B: Two.

A circle has many lines of symmetry. It has an infinite number of lines of symmetry. Every diameter of the circle is a line of symmetry.

Thus, the correct answer is Option D: Many.

• F does not have a vertical line of symmetry.
• T has a vertical line of symmetry. If you divide the letter vertically, both halves will be identical.
• E does not have a vertical line of symmetry.
• G does not have a vertical line of symmetry.

Thus, the correct answer is Option B: T.

Here, the given can be divided into two equal halves by the dotted lines shown in the figure above.
So, the number of lines of symmetry is 4.

In the △ ABC ,
Given: AB = AC
AD ⊥ BC, BE ⊥ AC and CF ⊥ AB
Since, AB = AC (given), the line AD will divide △ABC into two equal halves.
∴ △ABC is symmetrical about the line AD.

It is given that ABCD is a kite in which AB = AD and BC = DC.
A line of symmetry is a line that divides the form exactly in the half.
As we can see in the figure given below, we have a kite ABCD such that it has two diagonals AC and BD.
Here, the AC is bisecting the kite into equal parts.
But the second diagonal BD is not bisecting the kite into equal parts, therefore, it has only one line of symmetry which is diagonal AC. 

Hence, option (A) is the correct option.

The letter Z has no lines of symmetry. It is an asymmetrical letter, meaning it cannot be divided into two identical halves by any line (vertical, horizontal, or diagonal).

Thus, the correct answer is Option A: 0.

A rhombus is symmetrical about each of its diagonals. The diagonals of a rhombus bisect each other at right angles (90 degrees) and also act as lines of symmetry.

Thus, the correct answer is Option B: each of its diagonals.

The given figure does not have any line of symmetry.

The figure is a regular hexagon.

A regular pentagon has 5 equal sides. So the line passing through each vertex to the each opposite side will be a line of symmetry.

The symmetrical part of the given figure about the line l is the mirror image of the given figure.

The given figure has no line symmetry.

The question asks which of the following figures are symmetrical with respect to exactly two lines. Let’s analyze each figure:

1. Figure 1 (Star-like figure): This figure has four lines of symmetry. Hence, it is not symmetrical with respect to exactly two lines.

2. Figure 2 (Tree): This figure only has one line of symmetry (vertical symmetry), not two. Therefore, it does not meet the condition.

3. Figure 3 (Arrow pointing left and right): This figure has exactly two lines of symmetry: one vertical and one horizontal. Hence, this figure is symmetrical with respect to exactly two lines.

4. Figure 4 (Square): This figure has four lines of symmetry (two diagonals and two midlines). Therefore, it is not symmetrical with respect to exactly two lines.

Answer: The figure that is symmetrical with respect to exactly two lines is Figure 3 (the arrow pointing left and right)

A line of symmetry is a line that divides a figure into two corresponding parts, each of which is the mirror image of the other.
In the given figure, vertical and horizontal line which meet at the center of the figure are line of symmetry.
Also the lines which make the angle 45^o with vertical or horizontal lines are also line of symmetry for this figure. Hence the given Star have 4 line of symmetry.

The above figure has two lines of symmetry. One is horizontal AB and another one is vertical CD.

As shown in the figure only one minimum square should be shaded so that the figure has a line of symmetry.

Hence the correct answer is option A.

If you can reflect (or flip) a figure over a lime and the figure appears unchanged, then the figure has reflection symmetry or line symmetry. The line that you reflect over is called the line of symmetry. A line of symmetry divides a figure into two mirror-image halves.
In the given figure, lines ll and nn divide figure into two mirror-image halves.
Hence, they are lines of symmetries.