GSEB Class 7 Maths Solutions Chapter 14 Symmetry Exercise 14.1

Question 1. Copy the figures with punched holes and find the axes of symmetry for the following:
Answer: The axes of symmetry are shown by the dotted lines in the following figures:

Exam Tip: For punched holes, the axis of symmetry acts like a mirror line. If you fold the figure along this line, the punched holes should exactly overlap.

 

Question 2. Given the line(s) of symmetry, find the other hole(s):
Answer: The figures with other holes are given below:

Exam Tip: To find the other hole, imagine folding the paper along the line of symmetry. The missing hole must be at the exact spot where the given hole would land.

 

Question 3. In the following figures, the mirror line (i.e. the line of symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image.) Are you able to recall the name of the figure you complete?
Answer: The completed figures (i.e. the reflected figures) are given below along with the name of the figure:

Exam Tip: When completing a figure by reflection, make sure every point on the original shape has a corresponding point on the other side of the mirror line, at the same perpendicular distance.

 

Question 4. The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry. Identify multiple lines of symmetry, if any, in each of the following figures
Answer:

Exam Tip: To identify lines of symmetry, try to imagine folding the figure. If the two halves perfectly match along a fold line, that line is an axis of symmetry. Count all such unique lines.

 

Question 5. Copy the figure given here. Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals?
Answer:
(i) Let us take the diagonal AC and shade the squares as shown in the figure. The figure is symmetric about AC.

(ii) Since, the figure is symmetric about EF and GH also. Thus there are more than one way to make it symmetric.
(iii) The figure is symmetric about the diagonal BD also.

The figure is symmetric about both the diagonals.
In simple words: Yes, you can shade the squares so the figure is symmetric about either diagonal. You can also shade it so it's symmetric about both diagonals. Just make sure the shaded pattern mirrors itself across the diagonal line.

Exam Tip: When making a figure symmetric about a diagonal, ensure that if a square is shaded on one side of the diagonal, its mirror image square on the other side is also shaded.

 

Question 6. Copy the diagram and complete each shape to be symmetric about the mirror line(s):
Answer:

Exam Tip: For complex shapes on a grid, count squares or use coordinate points to ensure the reflected part is precisely drawn on the opposite side of the mirror line.

 

Question 7. State the number of lines of symmetry for the following figures:
Answer:
(a) An equilateral triangle has 3 lines of symmetry.
(b) An isosceles triangle has 1 line of symmetry.
(c) A scalene triangle has 0 line of symmetry.
(d) A square has 4 lines of symmetry.
(e) A rectangle has 2 lines of symmetry.
(f) A rhombus has 4 lines of symmetry.
(g) A parallelogram has 0 line of symmetry.
(h) A quadrilateral has 0 line of symmetry.
(i) A regular hexagon has 6 lines of symmetry.
(j) A circle has infinitely many lines of symmetry.
In simple words: The number of lines of symmetry tells you how many ways you can fold a shape perfectly in half. Some shapes, like circles, can be folded in half in endless ways.

Exam Tip: Remember specific counts for common polygons: equilateral triangle (3), square (4), regular hexagon (6). For a circle, it's always infinite.

 

Question 8. What letters of the English alphabet have reflectional symmetry (i.e. symmetry related to mirror reflection) about
(a) a vertical mirror
(b) a horizontal mirror
(c) both horizontal and vertical mirrors
Answer:
(a) Letters of the English alphabet having reflectional symmetry about a vertical mirror are:
A, H, I, M, O, T, U, V, W, X and Y
(b) Letters of the English alphabet having reflectional symmetry about a horizontal mirror are:
B, C, D, E, H, I, O and X
(c) Letters of the English alphabet having reflectional symmetry about both horizontal and vertical mirrors are:
O, X, I and H
In simple words: Some letters look the same when you hold them up to a mirror vertically, some horizontally, and some look the same for both. This means they are symmetrical.

Exam Tip: To check for vertical symmetry, imagine a line down the middle of the letter. For horizontal symmetry, imagine a line across the middle. Only consider uppercase letters unless specified.

 

Question 9. Give three examples of shapes with no line of symmetry.
Answer:
(i) A scalene triangle
(ii) The letter F
(iii) A parallelogram
In simple words: Shapes that have no line of symmetry cannot be folded perfectly in half in any way.

Exam Tip: Always recall shapes that are irregular or skewed as good examples of figures lacking symmetry, such as a scalene triangle or a general quadrilateral.

 

Question 10. What other name can you give to the line of symmetry of
(a) an isosceles triangle?
(b) a circle?
Answer:
(a) Median
(b) Diameter.
In simple words: For an isosceles triangle, its line of symmetry is also called a median to the base. For a circle, any line of symmetry is known as a diameter.

Exam Tip: Understand that specific geometric terms sometimes overlap with "line of symmetry" for particular shapes, reflecting the properties of those figures.