# NCERT Solutions for Class 7 Maths Chapter 14 Symmetry (EX 14.1) Exercise 14.1

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**NCERT Solutions for Class 7 Maths Chapter 14 Symmetry (EX 14.1) Exercise 14.1**

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**Access NCERT Solutions for Class 7 Chapter 14 – Symmetry Exercise 14.1**

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**What will you learn in Class 7 Maths Chapter 14 Exercise 14.1 solutions of Extramarks?**

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**Contents of the CBSE Class 7 Chapter 14 Maths Exercise 14.1**

Chapter 14 is one of the most crucial chapters in Class 7. The chapter is on Symmetry. Studying this chapter significantly enhances students’ logical thinking skills. Class 7 Maths Chapter 14 Exercise 14.1 includes numerous questions that frequently appear in the examinations. Class 7th Maths Chapter 14 Exercise 14.1 includes a total of 10 questions. This exercise covers some fundamental concepts of Symmetry that students can learn from the Introduction. This exercise also covers the topic of Lines of Symmetry for Regular Polygons. This exercise includes questions where students are required to find the lines of symmetry. Students need to learn to find the right way of solving such questions. The solutions provided by Extramarks can help them in this regard. Practising these types of questions not only helps students in their Class 7 exams but also in the future. As these questions help students improve their analytical skills, they can help students in various competitive exams in the future. Therefore, it is important that students solve Exercise 14.1 to be able to succeed in future exams as well.

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**Q.1 ****Copy the figures with punched holes and find the axes of symmetry for the following:**

**Ans**

\text{The axes of symmetry in the given figures are as follows:}

**Q.2 **

$\mathrm{Given}\mathrm{the}\mathrm{line}\left(\mathrm{s}\right)\mathrm{of}\mathrm{symmetry},\mathrm{find}\mathrm{the}\mathrm{other}\mathrm{hole}(\mathrm{s}):$

**Ans**

**Q.3 **

$\begin{array}{l}\mathrm{In}\mathrm{the}\mathrm{following}\mathrm{figures},\mathrm{the}\mathrm{mirror}\mathrm{line}\\ (\mathrm{i}.\mathrm{e}.,\mathrm{the}\mathrm{line}\mathrm{of}\mathrm{symmetry})\mathrm{is}\mathrm{given}\mathrm{as}\mathrm{a}\mathrm{dotted}\mathrm{line}.\mathrm{Complete}\\ \mathrm{each}\mathrm{figure}\mathrm{performing}\mathrm{reflection}\mathrm{in}\mathrm{the}\mathrm{dotted}\left(\mathrm{mirror}\right)\mathrm{line}.\\ (\mathrm{You}\mathrm{might}\mathrm{perhaps}\mathrm{place}\mathrm{a}\mathrm{mirror}\mathrm{along}\mathrm{the}\mathrm{dotted}\mathrm{line}\mathrm{and}\\ \mathrm{look}\mathrm{into}\mathrm{the}\mathrm{mirror}\mathrm{for}\mathrm{the}\mathrm{image}).\mathrm{Are}\mathrm{you}\mathrm{able}\mathrm{to}\mathrm{recall}\mathrm{the}\\ \mathrm{name}\mathrm{of}\mathrm{the}\mathrm{figure}\mathrm{you}\mathrm{complete}?\end{array}$

**Ans**

\text{(a) It will be a square}\text{.}

\text{(b) It will be a triangle}\text{.} \text{}

\text{(c) It will be a Rhombus}\text{.}

\text{(d) It will be a Circle}\text{.} \text{}

\text{(e) It will be a Pentagon}\text{.} \text{}

\text{(f) It will be a Octagon}\text{.}

**Q.4 **

$\mathrm{The}\mathrm{following}\mathrm{figures}\mathrm{have}\mathrm{more}\mathrm{than}\mathrm{one}\mathrm{line}\mathrm{of}\mathrm{symmetry}.\mathrm{Such}\mathrm{figures}\mathrm{are}\mathrm{said}\mathrm{to}\mathrm{have}\mathrm{multiple}\mathrm{lines}\mathrm{of}\mathrm{symmetry}.$

$\mathrm{Identify}\mathrm{multiple}\mathrm{lines}\mathrm{of}\mathrm{symmetry},\mathrm{if}\mathrm{any},\mathrm{in}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{figures}.$

**Ans**

\begin{array}{l}\text{(a) The given figure has 3 lines of symmetry}\text{.}\\ \text{Therefore, it has multiple lines of symmetry}\text{.}\end{array}

\begin{array}{l}\text{(b) The given figure has 2 lines of symmetry}\text{.}\\ \text{Therefore, it has multiple lines of symmetry}\text{.}\end{array}

\begin{array}{l}\text{(c) The given figure has 3 lines of symmetry}\text{.}\\ \text{Therefore, it has multiple lines of symmetry}\text{.}\end{array} \begin{array}{l}\text{}\end{array}

\begin{array}{l}\text{(d) The given figure has 2 lines of symmetry}\text{.}\\ \text{Therefore, it has multiple lines of symmetry}\text{.}\end{array} \begin{array}{l}\text{}\end{array}

\begin{array}{l}\text{(e) The given figure has 4 lines of symmetry}\text{.}\\ \text{Therefore, it has multiple lines of symmetry}\text{.}\end{array}

\text{(f) The given figure has only 1 line of symmetry}\text{.} \begin{array}{l}\text{}\end{array}

\begin{array}{l}\text{(g) The given figure has 4 lines of symmetry}\text{.}\\ \text{Therefore, it has multiple lines of symmetry}\text{.}\end{array} \begin{array}{l}\text{}\end{array}

\begin{array}{l}\text{(h) The given figure has 6 lines of symmetry}\text{.}\\ \text{Therefore, it has multiple lines of symmetry}\text{.}\end{array}

**Q.5 **

$\begin{array}{l}\mathrm{Copy}\mathrm{the}\mathrm{figure}\mathrm{given}\mathrm{here}.\\ \mathrm{Take}\mathrm{any}\mathrm{one}\mathrm{diagonal}\mathrm{a}\mathrm{s\; a}\mathrm{line}\mathrm{of}\mathrm{symmetry}\mathrm{and}\mathrm{shade}\\ \mathrm{a}\mathrm{few}\mathrm{more}\mathrm{squares}\mathrm{to}\mathrm{make}\mathrm{the}\mathrm{figure}\mathrm{symmetric}\mathrm{about}\\ \mathrm{a}\mathrm{diagonal}.\mathrm{Is}\mathrm{there}\mathrm{more}\mathrm{than}\mathrm{one}\mathrm{way}\mathrm{to}\mathrm{do}\mathrm{that}?\mathrm{Will}\mathrm{the}\\ \mathrm{figure}\mathrm{be}\mathrm{symmetric}\mathrm{about}\mathrm{both}\mathrm{the}\mathrm{diagonals}?\end{array}$

**Ans**

\text{There is one more way to do it and it is given below:}

**Q.6 **

$\mathrm{Copy}\mathrm{the}\mathrm{diagram}\mathrm{and}\mathrm{complete}\mathrm{each}\mathrm{shape}\mathrm{to}\mathrm{be}\mathrm{symmetric}\mathrm{about}\mathrm{the\; m}\mathrm{irror}\mathrm{line}\left(\mathrm{s}\right):$

**Ans**

\text{The given figures can be completed about the given mirror lines as follows:}

**Q.7 **

$\begin{array}{l}\mathrm{State}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{lines}\mathrm{of}\mathrm{symmetry}\mathrm{for}\mathrm{the}\mathrm{following}\\ \mathrm{figure}:\\ \left(\mathrm{a}\right)\mathrm{An}\mathrm{equilateral}\mathrm{triangle}\left(\mathrm{b}\right)\mathrm{An}\mathrm{isosceles}\mathrm{triangle}\\ \left(\mathrm{c}\right)\mathrm{A}\mathrm{scalene}\mathrm{triangle}\left(\mathrm{d}\right)\mathrm{A}\mathrm{square}\\ \left(\mathrm{e}\right)\mathrm{A}\mathrm{rectangle}\left(\mathrm{f}\right)\mathrm{A}\mathrm{rhombus}\\ \left(\mathrm{g}\right)\mathrm{A}\mathrm{parallelogram}\left(\mathrm{h}\right)\mathrm{A}\mathrm{quadrilateral}\\ \left(\mathrm{i}\right)\mathrm{A}\mathrm{regularhexagon}\left(\mathrm{j}\right)\mathrm{A}\mathrm{circle}\end{array}$

**Ans**

\text{(a) There are 3 lines of symmetery in an equilateral triangle}\text{.}

\text{(b) There is only 1 line of symmetery in an isosceles triangle}\text{.}

(\text{c})\text{There is no line of symmetry in a scalene triangle}\text{.}

\text{(d) There are 4 lines of symmetery in a square}\text{.}

\text{(e) There are 2 lines of symmetry in a rectangle}\text{.}

\text{(f) There are 2 lines of symmetry in a rhombus}\text{.}

\text{(g) There is no line of symmetry in a parallelogram}\text{.}

\text{(h) There is no line of symmetry in a quadrilateral}\text{.}

\text{(i) There are 6 lines of symmetery in a regular hexagon}\text{.}

**Q.8**

$\begin{array}{l}\mathrm{What}\mathrm{letters}\mathrm{of}\mathrm{the}\mathrm{English}\mathrm{alphabet}\mathrm{have}\mathrm{reflectional}\\ \mathrm{symmetry}(\mathrm{i}.\mathrm{e}.,\mathrm{symmetry}\mathrm{related}\mathrm{to}\mathrm{mirror}\mathrm{reflection})\\ \mathrm{about}.\\ \left(\mathrm{a}\right)\mathrm{a}\mathrm{vertical}\mathrm{mirror}\\ \left(\mathrm{b}\right)\mathrm{a}\mathrm{horizontal}\mathrm{mirror}\\ \left(\mathrm{c}\right)\mathrm{both}\mathrm{horizontal}\mathrm{and}\mathrm{vertical}\mathrm{mirrors}.\end{array}$

**Ans**

\text{(a) A, H, I,M, O, T, U, V, W, X, Y are the letters having a reflectional symmetry about a vertical mirror}\text{.}

\text{(b) B, C, D, E, H, I, K, O, X are the letters having a reflectional symmetry about a horizontal mirror}\text{.} \text{}

\text{(c) H,I,O,X are the letters having a reflectional symmetry about horizontal and vertical mirror}\text{.}

**Q.9 **

$\mathrm{Give}\mathrm{three}\mathrm{examples}\mathrm{of}\mathrm{shapes}\mathrm{with}\mathrm{no}\mathrm{line}\mathrm{of}\mathrm{symmetry}.$

**Ans**

\text{A scalene triangle, a parallelogram and a trapezium have no line of symmetry}\text{.}

**Q.10 **

$\begin{array}{l}\mathrm{What}\mathrm{other}\mathrm{name}\mathrm{can}\mathrm{you}\mathrm{give}\mathrm{to}\mathrm{the}\mathrm{line}\mathrm{of}\mathrm{symmetry}\mathrm{of}\\ \left(\mathrm{a}\right)\mathrm{an}\mathrm{isosceles}\mathrm{triangle}?\\ \left(\mathrm{b}\right)\mathrm{a}\mathrm{circle}?\end{array}$

**Ans**

\begin{array}{l}\text{(a) An isosceles triangle has one line of symmetry}\text{.}\\ \text{Therefore, this line of symmetry is the median and also the}\\ \text{altitude of the isosceles triangle}\text{.}\end{array}

\begin{array}{l}\text{(b) In a circle, there are infinite lines of symmetry}\text{.}\\ \text{Some of which are represented as below:}\end{array}