# NCERT Solution Class 6 Maths Chapter -13 Symmetry

**Exercise 13. 1**

**Q1. Observe your surroundings in school or home and list some symmetrical objects.**

** Ans:**

CD, Glass, Paper sheet, Bucket, Bathtub

**Q2. Find out the mirror line,for the figure given below.**

**Ans:** In the given figure, line l2 is the mirror line. The left and right part of the object is same when folded about the line l2.

**Q3. From given figure, identify the shapes of the objects and check if they are symmetrical in nature. Also, draw the symmetry line.**

**Ans:**

(a) Symmetry

(b) Symmetry

(c) Asymmetry

(d) Symmetry

(e) Symmetry

(f) Symmetry

The symmetry line for each shape is given below

**Q4. Draw the other part of the object with the symmetric axis as areference, on a squared paper.**

**Ans:** Considering the symmetry line, the given figures can be drawn as follows

**(a)**

**(b)**

**(c)**

**(d)**

**(e)**

**(f)**

**Q5.In the figure given below, l is the symmetry line. Complete the figure, such that the diagram becomes symmetrical.**

**Ans:** To make the figure symmetric, it can be drawn as follows

**Q6.Draw the image of the triangle and complete the figure so that it becomes symmetrical.**

**Ans:**

**Exercise 13.2**

Q1. Find the number of symmetrical lines for the each figure given below by drawing the lines.

**Ans:**

(a) There are total 4 lines of symmetry in the given figure.

(b) There are total 4 lines of symmetry in the given figure.

(c) There are total 4 lines of symmetry in the given figure.

(d) There is only 1 line of symmetry in the given figure.

(e) There are total 6 lines of symmetry in the given figure.

(f) There are total 6 lines of symmetry in the given figure.

(g) There is no line of symmetry in the given figure.

(h) There is no line of symmetry in the given figure.

(i) There are total 3 lines of symmetry in the given figure.

The line of symmetry in the above figures can be represented as follows

**Q2. Draw the line of symmetry.**

**Ans:**

l1 is the line of symmetry.

l1 is the line of symmetry.

l1 is the line of symmetry.

No line of symmetry

**Q3.Complete the tablegiven below:**

**Ans:** The above table can be completed as follows

In the case of a circle, there can be an infinite number of lines. In the above table, only some lines of symmetry are drawn. More line of symmetry can be similarly drawn from it.

**Q4.Is it possible to draw a triangle which**

**(a) has only one line of symmetry?**

**(b) has exactly 2 lines of symmetry?**

**(c) has exactly 3 lines of symmetry?**

**(d) has no lines of symmetry?**

**Sketch the rough figure in each case**

**Ans:**

(a) Yes, we can make an isosceles triangle which has 1 line of symmetry.

(b) No, we can’t draw such a triangle.

(c) Yes, we can make an equilateral triangle which has 3 symmetrical lines.

(d) Yes, we can make a scalene triangle which has no line of symmetry.

**Q5.Can you draw the following?**

**(a) A triangle having no vertical symmetrical line but has a line of symmetry in the horizontal direction.**

**(b) A quadrilateral having both vertical and horizontal symmetrical line.**

**(c) A quadrilateral with a horizontal line but no vertical line of symmetry.**

**(d) A hexagon having exactly 2 lines of symmetry.**

**(e) A hexagon having 6 lines of symmetry.**

**Ans: (a)** A triangle with only 1 horizontal line of symmetry and no other vertical lines of symmetry can be sketched as follows.

**(b)** A quadrilateral with both horizontal and vertical lines of symmetry can be drawn as follows.

**(c)** A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry can be drawn as follows.

**(d)** A hexagon with exactly 2 lines of symmetry can be sketched as follows.

**Q6. Trace each figure and draw the lines of symmetry, if any**

**Ans:**

**(a)** The given figure is an isosceles triangle. Therefore, there will be one line of symmetry.

**(b)** The given figure has two line of symmetry.

**(c)** The given figure has four line of symmetry.

**(d)** The given figure has only one line of symmetry.

**(e)** The given figure has four line of symmetry.

**Q7.How many among the letters of English alphabet have**

**(a) lines of symmetry in the vertical direction (like A)?**

**(b) lines of symmetry in the horizontal direction (like B)?**

**(c) no lines of symmetry (like Q)?**

**Ans:**

(a) A, H, I, M. 0, T, U, V, W, X,

(b) B, C, 0, E, H, I, K, 0,X

(c) F, G4, L, N, P, Q, R. 5, Z

**Q8. The figure given below is drawn on a folded sheet, draw the rough image of how it would look like when the designs are cut off.**

**Ans:**

**The complete figure is as follows:**

**Exercise 7.3**

**Q1. In the following shapes, how many lines of symmetry are there?**

**Ans. **

**(a)** The given figure has four symmetrical lines.

**(b)** The given figure has one symmetrical line.

**(c)** The given figure has two symmetrical lines.

**(d)** The given figure has two symmetrical lines.

**(e)** The given figure has one symmetrical line.

**(f)** The given figure has two symmetrical lines.

**Q2. In the given figure, a vertical line is drawn next to the alphabet. Take the mirror image of it. Which letters look alike after reflection and tell why is that?**

**Check for A, B, O, E, M, N, P, H, L, T, S, V and X.**

**Ans:**

The letters, which have the mirror image of each other, are A, O, M, N, H, T, X, V.