Linear Symmetry Class 6 ICSE — Maths Chapter 22
Linear symmetry class 6 ICSE appears in Chapter 22 of the ICSE Mathematics textbook. The chapter explains what a line of symmetry is, how to recognise it in everyday shapes, and how to construct symmetric points. You will learn the mirror idea, the paper folding test, and the perpendicular bisector method. Each section below follows the book’s own order and numbering.
Download Linear Symmetry Class 6 ICSE Mathematics Chapter 22 PDF
Download the Linear Symmetry Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 5 pages, 4 sections.
What is inside Chapter 22
5 pages · 4 sections
| Section | Title |
|---|---|
| 22.1 | CONCEPT OF SYMMETRY (LINEAR SYMMETRY) |
| 22.2 | SYMMETRIC POINT |
| 22.3 | TO LOCATE A POINT THAT IS SYMMETRIC TO A GIVEN POINT WITH RESPECT TO A GIVEN LINE |
| 22.4 | CONSTRUCTING THE LINE OF SYMMETRY WHEN TWO FIXED POINTS ARE SYMMETRIC WITH RESPECT TO THE REQUIRED LINE |
22.1 CONCEPT OF SYMMETRY (LINEAR SYMMETRY)
The chapter opens with a plane mirror. Suppose an object F sits at distance d in front of the mirror mm’. Its image F’ forms at the same distance d behind the mirror. When you fold the figure along mm’, the object and its image coincide. That fold line is the mirror line, and the whole figure is symmetrical about it.
A paper folding activity makes the idea clearer. Fold a rectangular sheet of paper, cut a design from the folded side, then unfold. The pattern on both sides of the crease AB is identical. So AB is the line of symmetry. A figure identical on both sides of a line is symmetrical about that line, and that line is called the line of symmetry or the axis of symmetry.
The chapter lists common figures with their line counts:
| Figure | Lines of symmetry |
|---|---|
| Line segment | one (its perpendicular bisector) |
| Angle with equal arms | one (its bisector) |
| Isosceles triangle | one |
| Equilateral triangle | three |
| Kite-shaped figure | one |
| Arrow-head | one |
| Letter A | one |
| Letter H | two |
| Circle | infinite |
A circle has an infinite number of lines of symmetry. Every line that passes through its centre is a line of symmetry. You can study more circle properties in the Class 6 Maths circle chapter.
Worked pattern: draw an isosceles triangle with two sides 6 cm each and a base of 8 cm. Its single line of symmetry is the bisector of the angle between the two equal sides. That line also cuts the base into two equal halves of 4 cm each. A scalene triangle, by contrast, has no line of symmetry because no two sides are equal.
Common mistake: the letters N and F have no line of symmetry. Do not assume every capital letter is symmetrical. Folding N or F along any line never makes the two halves match.
22.2 SYMMETRIC POINT
This section defines what makes two points symmetric. Take a point P and a line AB. From P, draw PO perpendicular to AB. Then extend PO to Q so that OP = OQ. When you fold the figure about AB, points P and Q coincide.
So Q is the symmetric point of P with respect to the line AB. In fact, P and Q are symmetric to each other about AB. Line AB is the perpendicular bisector of the segment PQ. It is also the line of symmetry of the whole figure.
Worked pattern: place point P at a distance of 3 cm from line AB. Draw PO perpendicular to AB. Measure 3 cm past O on the other side and mark Q. Now OP = OQ = 3\ \text{cm}. Folding about AB makes P land exactly on Q.
22.3 TO LOCATE A POINT THAT IS SYMMETRIC TO A GIVEN POINT WITH RESPECT TO A GIVEN LINE
This section turns the idea into a construction. Given a point P and a line AB, you want the point Q symmetric to P about AB. Follow these steps:
- Draw PO perpendicular to AB.
- Extend PO beyond O.
- Cut OQ equal to OP.
Then Q is the point symmetric to P with respect to AB. The perpendicular must be drawn first, because O is the foot of the perpendicular on AB. Every later measurement depends on it.
To check your construction, fold the figure about AB. If the work is correct, P and Q fall on the same spot.
Worked pattern: draw a line AB, 5 cm long. Mark point P, 2.5 cm away from AB. Draw PO perpendicular to AB. Extend PO and cut OQ = OP = 2.5\ \text{cm}. Point Q is the symmetric point, and folding along AB confirms it.
22.4 CONSTRUCTING THE LINE OF SYMMETRY WHEN TWO FIXED POINTS ARE SYMMETRIC WITH RESPECT TO THE REQUIRED LINE
Here the problem is reversed. You are given two fixed points P and Q. You must construct the line that makes them symmetric. The method has two steps:
- Join P and Q.
- Draw the perpendicular bisector of segment PQ.
That perpendicular bisector AB is the required line of symmetry. With respect to AB, the points P and Q are symmetric. Any point on the bisector is equidistant from P and Q, which is why folding along AB makes the two points coincide.
Worked pattern: mark two points A and B, 5.5 cm apart, as in practice question 9. Join them and draw the perpendicular bisector of AB. That bisector is the line of symmetry, and its special name is the perpendicular bisector of segment AB. The full list of Class 6 ICSE Maths chapters is in the Mathematics book hub.
What to practise from Linear Symmetry Class 6 ICSE
The exercise after section 22.4 has 12 questions. They group by skill:
- Q1: state true or false on letters and triangles.
- Q2, Q10, Q11, Q12: draw all lines of symmetry in letters, the alphabet and shaded figures.
- Q3, Q5, Q6: construct a triangle with given side lengths and draw its lines of symmetry. Q6 uses \angle ABC = 60^\circ.
- Q4, Q7: draw lines of symmetry in given figures.
- Q8: construct a point symmetric to P about line AB.
- Q9: mark two points 5.5 cm apart and name the special line.
These questions follow the pattern set out in the official CISCE syllabus.
Linear Symmetry Class 6 ICSE frequently asked questions
What is linear symmetry in Class 6 ICSE Maths?
Linear symmetry means a figure has a line about which its two halves are identical. When you fold the figure along that line, both parts coincide. The line is called the line of symmetry or the axis of symmetry.
How many lines of symmetry does a circle have?
A circle has an infinite number of lines of symmetry. Every line that passes through the centre of the circle is a line of symmetry.
Why does the letter N have no line of symmetry?
Folding the letter N along any line never makes its two halves match. The parts on either side of any fold do not coincide. So N has no line of symmetry.
How do you locate a point symmetric to a given point about a line?
Draw a perpendicular from the point to the line. Extend it past the line, then cut off a length equal to the original distance. The new point is the symmetric point.
How do you construct the line of symmetry when two fixed points are given?
Join the two points and draw the perpendicular bisector of the segment. That bisector is the line of symmetry. Any point on it is equidistant from both given points.
Reference: ICSE Class 6 Mathematics textbook material, chapter 22: Linear Symmetry — CISCE-aligned.