GSEB Class 6 Maths Solutions Chapter 13 સંમિતિ InText Questions

Exercise: (Page Number 262)

Question 1. There are two triangular instruments in your compass box. Are they symmetrical?
Answer: In our compass box, we find two different types of triangular set squares.
(i) A set square having angles of \( 30^\circ \), \( 60^\circ \), and \( 90^\circ \).
(ii) A set square having angles of \( 45^\circ \), \( 45^\circ \), and \( 90^\circ \).
Out of these two types of set squares, the second one, which has angles \( 45^\circ \), \( 45^\circ \), and \( 90^\circ \), is symmetrical. However, the first set square, which features angles \( 30^\circ \), \( 60^\circ \), and \( 90^\circ \), is not symmetrical.
In simple words: The set square with two 45-degree angles is symmetrical, meaning you can fold it in half perfectly. The one with 30 and 60-degree angles is not symmetrical, so it won't fold evenly.

Exam Tip: Remember that a shape is symmetrical if it can be divided into two identical halves by a line of symmetry. Test this by folding or drawing a line through the shape.

Exercise: (Page Number 264)

Question 1. Make as many shapes as possible by combining two or more set squares. Draw them on square grid paper and determine their line of symmetry.
Answer:
(a) When we place two identical set squares from the compass box, each having \( 30^\circ \), \( 60^\circ \), and \( 90^\circ \) angles, side by side, the following four shapes are created:
(i) When arranged as demonstrated here, a rectangle is formed. This rectangle possesses two lines of symmetry, labeled \( I_1 \) and \( I_2 \), as indicated.
(ii) When arranged as displayed here, a kite is created. This kite features only one line of symmetry, which is marked by \( m \).
(iii) When arranged as demonstrated here, a parallelogram is formed. This parallelogram has only one line of symmetry, which is denoted by \( n \).
(iv) When arranged as shown here, an isosceles right triangle is created. This isosceles right triangle has only one line of symmetry, which is indicated by \( l \).
(b) When two identical set squares from the compass box, each having \( 45^\circ \), \( 45^\circ \), and \( 90^\circ \) angles, are positioned side by side, the following two figures are formed:
(i) When arranged as shown here, a square is formed. This square features four lines of symmetry, which are indicated by \( I_1 \), \( I_2 \), \( I_3 \), and \( I_4 \).
(ii) When arranged as displayed here, an isosceles right triangle is created. This isosceles right triangle features one line of symmetry, which is indicated by \( l \).
(c) When three identical set squares from the compass box, each having \( 45^\circ \), \( 45^\circ \), and \( 90^\circ \) angles, are placed side by side, the figure shown below is formed. It has one line of symmetry, which is indicated by \( l \).
In simple words: By joining two or more set squares, you can make many shapes like rectangles, kites, parallelograms, and triangles. Each of these shapes can have lines where you can fold them perfectly in half. Some shapes have many lines of symmetry, while others only have one.

Exam Tip: Practice drawing different combinations and identifying all possible lines of symmetry. Use tracing paper or actual set squares to visualize the transformations.

HOTS Type Questions

For the answer to each of the following questions, find the correct option from the given alternatives and write its serial letter in the box provided next to the question.

Question 1. A scalene triangle has ............ line of symmetry.
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (a) 0
In simple words: A scalene triangle has no sides or angles that are the same, so it cannot be folded perfectly in half. This means it has zero lines of symmetry.

Exam Tip: Remember the properties of different types of triangles. A scalene triangle is defined by having all sides of different lengths, which inherently means no symmetry.

Question 2. An isosceles triangle has ................ line of symmetry.
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b) 1
In simple words: An isosceles triangle has two sides of equal length. Because of this, it has exactly one line of symmetry, which runs from the vertex between the equal sides to the midpoint of the base.

Exam Tip: Visualize an isosceles triangle; the line of symmetry always bisects the angle between the two equal sides and the opposite base.

Question 3. The reflection of ................ looks like the original letter.
(a) A
(b) S
(c) C
(d) N
Answer: (a) A
In simple words: When you look at the reflection of the letter 'A' in a mirror, it still appears like the letter 'A'. This is because 'A' has a vertical line of symmetry.

Exam Tip: To determine if a letter's reflection looks like the original, check if it has a vertical line of symmetry. Letters like A, H, I, M, O, T, U, V, W, X, Y appear unchanged in a mirror.

Question 4. The reflection of ................ does not look like the original letter.
(a) 0
(b) M
(c) N
(d) A
Answer: (c) N
In simple words: When you look at the letter 'N' in a mirror, its reflection will appear flipped or backward, and it won't look exactly like the original 'N'. This is because 'N' does not have a vertical line of symmetry.

Exam Tip: For letters whose reflection does not look like the original, they generally lack both vertical and horizontal lines of symmetry (e.g., N, S, Z, F, G, J, L, P, Q, R).

Question 5. A circle has ................ lines of symmetry.
(a) 1
(b) 2
(c) 4
(d) Infinite
Answer: (d) Infinite
In simple words: A circle is perfectly round, so you can draw an endless number of lines right through its center, and each line will divide the circle into two identical halves. Therefore, it has countless lines of symmetry.

Exam Tip: Any line passing through the center of a circle is a line of symmetry. Since there are infinitely many such lines, a circle has infinite lines of symmetry.

Question 6. A square has ................ lines of symmetry.
(a) 4
(b) 3
(c) 2
(d) 1
Answer: (a) 4
In simple words: A square has four equal sides and four right angles. It can be folded perfectly in half along its two diagonals and also along the lines connecting the midpoints of opposite sides. This gives it a total of four lines of symmetry.

Exam Tip: For regular polygons, the number of lines of symmetry is equal to the number of sides. A square is a regular polygon with four sides, hence four lines of symmetry.