Basic Geometry — Shapes & Symmetry • Topic 4 of 4

Symmetry

Symmetry is balance — a figure that can be split into two halves that mirror each other exactly. The straight line you fold along is the line of symmetry, and the test is simple: fold the figure on that line and the two halves should land perfectly on top of one another. This is why teachers reach for paper-folding the moment they introduce the idea; a child can cut out a shape, fold it, and literally see whether the halves coincide. Different shapes carry different numbers of these fold lines. A circle has infinitely many, since every line through its centre works. A square has 4 (two through the midpoints of opposite sides and two along the diagonals), a rectangle has 2 (only through the midpoints of opposite sides — never along a diagonal), an equilateral triangle has 3, and an isosceles triangle has just 1, from its apex to the middle of the base. A scalene triangle has none. Closely linked is the mirror image, the reflection you see in a looking glass, where left and right swap over — what we call lateral inversion. So lowercase 'b' reflects into 'd'. CTET ties all of this to things children already know — butterfly wings, rangoli patterns, the symmetry of letters like A, M and T, and digits like 8 — which keeps the learning hands-on and in step with the NCF\'s push for experiential teaching.

✅ Solved examples

1. How many lines of symmetry does a circle have?
Infinitely many. Every straight line that passes through the centre divides the circle into two identical halves.
2. Does a rectangle have a diagonal line of symmetry?
No. A rectangle has exactly 2 lines of symmetry, both running through the midpoints of opposite sides. Folding along a diagonal does not make the halves coincide.
3. What does a mirror image do to a figure, and what is that effect called?
It swaps left and right while keeping top and bottom the same. This left-right reversal is called lateral inversion.
4. Which has exactly one line of symmetry: a square or an isosceles triangle?
The isosceles triangle. Its single line of symmetry runs from the apex to the midpoint of the base. A square has 4 lines of symmetry.

✏️ Practice — try these, take hints as needed

1. A line of symmetry divides a figure into how many parts, and how do they compare?
Picture folding the figure along the line.
The parts must land on top of each other.
Two parts that are exactly matching mirror halves
2. How many lines of symmetry does a regular pentagon have?
A regular polygon has as many lines as it has sides.
Each line runs from a vertex to the opposite side.
5
3. In a paper-folding activity a child folds a cut-out and the two halves do NOT coincide. What can the child conclude about the figure?
Coinciding halves would mean it is symmetric.
No matching fold line means no symmetry.
The figure is asymmetric (it has no line of symmetry)
4. The line of symmetry of a butterfly usually runs in which direction?
The two wings are mirror images.
The fold line goes down the middle of the body.
Vertical (down the centre of the body)

📝 Topic test — 8 questions

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