Symmetry Sums for Class 6 — Free CBSE Worksheet PDF with Answers

Look at a butterfly. Fold it down the middle and both halves match. That fold line is a line of symmetry. You will find symmetry in leaves, buildings, rangoli designs, the Taj Mahal, and even the letters of the alphabet. The Class 6 CBSE Symmetry chapter teaches you to spot, count, and draw lines of symmetry — and to complete a half-figure to make a symmetric whole.

A line of symmetry divides a figure into two halves that are mirror images of each other. Some shapes have one line, some have several, and a circle has infinitely many. This chapter is mostly visual, which makes it a strong score-booster for Class 6 students who do well with diagrams.

This worksheet has 60 questions across three levels. Level 1 covers counting lines of symmetry and identifying symmetric figures. Level 2 has students draw lines of symmetry and complete half-figures. Level 3 tackles multiple lines, pattern completion, and reasoning.

Regular polygons have as many lines of symmetry as they have sides. An equilateral triangle has $3$ lines of symmetry — one from each vertex through the midpoint of the opposite side. A square has $4$ — two through midpoints of opposite sides, and two along the diagonals. A regular pentagon has $5$, a regular hexagon has $6$, and so on.

A general rectangle (non-square) has only $2$ lines of symmetry — one horizontal through the midpoints of long sides, one vertical through the midpoints of short sides. Diagonals of a rectangle are not lines of symmetry (folding along a diagonal does not give matching halves). A rhombus has $2$ lines (the two diagonals). A circle has infinitely many lines — every diameter is a line of symmetry.

Many capital letters of the English alphabet have symmetry. A, M, T, U, V, W, Y have a vertical line of symmetry. B, C, D, E, K have a horizontal line of symmetry. H, I, O, X have both. The letter O is also rotationally symmetric. F, G, J, L, N, P, Q, R, S, Z have no line of symmetry.

A scalene triangle (all sides different) has no line of symmetry. An isosceles triangle (two sides equal) has $1$ line of symmetry — the axis through the vertex angle and the midpoint of the base. An equilateral triangle has $3$. A general parallelogram has no line of symmetry (folding any way does not give matching halves), but special parallelograms — rectangles, rhombuses, squares — do.

Many CBSE Class 6 questions show half a figure with a line of symmetry drawn, and ask you to complete the other half. The technique: for each point of the given half, count perpendicular distance to the line of symmetry. Mirror that distance on the other side and mark the corresponding point. Connect the mirrored points in the same order to complete the figure.

Use grid paper for these questions whenever possible — counting squares makes the mirroring much easier. For a rangoli pattern with $4$ lines of symmetry, you only need to design one quarter; the other three quarters are forced by symmetry.