Q1.
Take a piece of square paper and fold it in different ways. Now, on the creases formed by the folds, draw lines using a pencil and a scale. You will notice different lines on the paper. Take any pair of lines and observe their relationship with each other. Do they meet? If they do not meet within the paper, do you think they would meet if they were extended beyond the paper?
Answer
Some pairs of creases cross inside the paper — those lines meet. Other pairs do not cross inside the paper, and for those there are two very different possibilities.
- If the two creases are slanted differently, the gap between them keeps shrinking on one side. Extend them beyond the paper and they will meet.
- If the two creases keep exactly the same gap everywhere (for example, the two creases you get by folding the sheet in half twice), they will never meet, however far you extend them. Such lines are parallel.
Why it happens: Two straight lines in a plane can cross at most once. So either they already cross, or they cross somewhere outside the paper, or they never cross at all. The only way they never cross is if they lean at exactly the same angle — then the distance between them stays the same for ever.
Check it yourself: Lay a ruler along one crease and slide it towards the other, keeping it parallel. If the two creases stay the same distance apart all along the ruler, they will never meet.