EN हिं

NCERT Solutions for Class 7th Maths Chapter 5 Activity 2 — Parallel and Perpendicular Lines in Paper Folding

Book page 111 Updated on2026-09-19

Q1.
Take a plain square sheet of paper (use a newspaper for this activity). How would you describe the opposite edges of the sheet? They are _________________________ to each other.
Answer

The opposite edges of the sheet are parallel to each other.

Why it happens: The left and right edges of a square sheet stay exactly the same distance apart (the side length) all the way from top to bottom. Lines in a plane that keep a constant gap can never meet, so they are parallel.
Q2.
How would you describe the adjacent edges of the sheet? The adjacent edges are _________________________ to each other. They meet at a point. They form right angles.
Answer

The adjacent edges are perpendicular to each other.

Each corner of the sheet is a right angle
Angle between two adjacent edges = 90°
Why it happens: A square (or a rectangle) has four right-angled corners. Two edges that meet at a corner cross at 90°, which is exactly the meaning of perpendicular.
Q3.
Fold the sheet horizontally in half. A new line is formed (see Fig. 5.7). How many parallel lines do you see now? How does the new line segment relate to the vertical sides?
Fig. 5.7, page 111 — folding a square sheet horizontally in half, then again, then once more, and finally a vertical fold.
Answer

You now see 3 parallel lines — the top edge, the new crease, and the bottom edge.

2 horizontal edges + 1 crease = 3 parallel lines

The new crease is perpendicular to the two vertical sides, and it cuts each of them exactly in half.

Why it happens: Folding the top edge down onto the bottom edge makes the crease run in exactly the same direction as those edges, so all three are parallel. Since the vertical sides were already perpendicular to the top and bottom edges, they are perpendicular to the crease as well.
Q4.
Make one more horizontal fold in the folded sheet. How many parallel lines do you see now?
Answer

5 parallel lines.

Folding the already-folded sheet in half makes 3 creases in all
3 creases + 2 horizontal edges = 5 parallel lines
Why it happens: The single crease you already had is copied on both halves of the new fold, so one crease becomes three. Every one of them runs parallel to the top and bottom edges.
Q5.
What will happen if you do it once more? How many parallel lines will you get? Is there a pattern? Check if the pattern extends further, if you make another horizontal fold.
Answer

After a third fold you get 9 parallel lines, and after a fourth fold 17.

Number of folds, nCreasesParallel lines
113
235
379
41517
Creases after n folds = 2n – 1
Parallel lines = creases + 2 edges
= (2n – 1) + 2
= 2n + 1
Why it happens: Each new fold doubles the number of layers, so every existing crease is copied once and one brand-new crease is added in the middle. That is why the crease count goes 1 → 3 → 7 → 15, each time doubling and adding one.
Note: The pattern is 2n + 1 (2, raised to the power n), not 2 × n + 1. For n = 3 the formula 2 × 3 + 1 would give 7, but folding really gives 9 lines — count them on your own sheet.
Q6.
Make a vertical fold in the square sheet. This new vertical line is ___________ to the previous horizontal lines.
Answer

This new vertical line is perpendicular to the previous horizontal lines.

Vertical crease meets each horizontal crease at 90°
Why it happens: The vertical fold brings the left edge onto the right edge, so the crease runs in the direction of the vertical sides. Those sides are perpendicular to the horizontal creases, so the new crease is perpendicular to all of them.
Tip: All the horizontal creases are parallel to one another, so a single line perpendicular to one of them is automatically perpendicular to all of them.
Q7.
Fold the sheet along a diagonal. Can you find a fold that creates a line parallel to the diagonal line?
Answer

Yes. Here is one easy way for a square sheet ABCD with the diagonal crease AC.

  1. Fold along both diagonals once to mark the centre O of the square.
  2. Now fold corner B so that it lands exactly on O.
  3. Unfold. The new crease is parallel to the diagonal AC.
Why it happens: B is carried to O along the line BD, which is perpendicular to AC. A fold moves a point straight across the crease, so the crease must be perpendicular to BD — and any line perpendicular to BD runs in the same direction as AC. Same direction means parallel.
Try This: Fold B onto the midpoint of BO instead. You get another crease parallel to AC, but closer to B. In fact every fold that takes B to a point of BD gives a line parallel to AC.
Was this helpful?