Olympiad Test: Symmetry - Class 6 MCQ

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.