NCERT Solutions Ganita Prakash Chapter 9 Paper Folding and Cutting — In-text Questions
Book page 223 Updated on2026-09-05
Q1.
In these two figures, a sheet of paper is folded and a cut is made along the dotted line shown. Draw a sketch of how the paper will look when unfolded. Do you see a line of symmetry in this figure? What is it?
Answer
The cut is made starting from the folded edge, so the piece that falls out is only half of the hole. When the paper is opened, that half is joined by its mirror image and a complete hole appears in the middle of the sheet.
Left: the folded sheet with the dotted cut. Right: the opened sheet — the hole is the cut shape together with its mirror image.
Yes, the opened figure has a line of symmetry — it is exactly the crease (the fold line). Everything on the right of the crease is the mirror image of everything on its left, hole included.
Tip: the shape of the hole is always “the cut piece + its mirror image”. So if you cut half a heart at the fold, you open out a full heart; half a star gives a full star.
Q2.
Use thin rectangular coloured paper. Fold it several times and create some intricate patterns by cutting the paper, like the one shown here. Identify the lines of symmetry in the repeating design. Use such decorative paper cut-outs for festive occasions.
Answer
Fold a long strip of thin paper like a fan (accordion folds), cut a small design through all the layers at once, and open it out. You get the same design repeated again and again along the strip.
Each cut passes through every layer, so one snip makes as many copies as there are layers. Four folds give 16 layers and 16 copies!
Every crease is a line of symmetry of the finished strip — the design on one side of a crease is the mirror image of the design on the other side.
In the printed design each blue star also has its own lines of symmetry: an eight-pointed star has 8, and each small diamond has 2.
Two kinds of pattern in one strip: the whole strip repeats by sliding (translation) along its length, and each repeat is a mirror of its neighbour. That is why the border looks so neat.
Try This: make such a paper toran for Diwali or a birthday. Fold, cut a half-flower on the crease, open — a whole row of flowers appears.