Parallel and Intersecting Lines | A

Question 1

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?

Solution

We will observe how different lines in the diagram relate to each other.

Step 1 — Observing Intersecting Lines

Let us pick two lines from the diagram. We can see two main diagonal lines. One line goes from the top-left corner. It goes down to the bottom-right corner. The other line goes from the top-right corner. It goes down to the bottom-left corner. These two lines cross each other at one point. This point is inside the square paper. Lines that cross at a point are called intersecting lines. So, these two diagonal lines are intersecting lines.

Diagram 1

Step 2 — Observing Parallel Lines

Now, let us pick another pair of lines. We can see two vertical dashed lines. These lines run from the top edge. They go down to the bottom edge. They are always the same distance apart. These lines do not meet inside the paper. If we extend these lines, they will still not meet. Lines that never meet, even when extended, are called parallel lines. So, these two vertical lines are parallel lines.

Diagram 2

Answer

(i) Yes, some pairs of lines meet within the paper. (ii) If lines do not meet within the paper, some would meet if extended. (iii) Other lines would never meet, even if extended beyond the paper.

More questions in A

Draw two lines on a plain sheet of paper so that they intersect. Measure the four angles formed with a protractor. Draw four such pairs of intersecting lines and measure the angles formed at the points of intersection.

What patterns do you observe among these angles?

Activity 2 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.
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.
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?
Make one more horizontal fold in the folded sheet. How many parallel lines do you see now?
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.
Make a vertical fold in the square sheet. This new vertical line is _______________________ to the previous horizontal lines.
Fold the sheet along a diagonal. Can you find a fold that creates a line parallel to the diagonal line?

Here is another activity for you to try.

Take a square sheet of paper, fold it in the middle and unfold it.
Fold the edges towards the centre line and unfold them.
Fold the top right and bottom left corners onto the creased line to create triangles. Refer to Fig. 5.8.
The triangles should not cross the crease lines.
Are $a$ , $b$ and $c$ parallel to $p$ , $q$ and $r$ respectively? Why or why not?

Draw a pair of lines and a transversal such that they form two distinct angles.

Fig. 5.19 has a pair of parallel lines $l$ and $m$ (what is the notation used in the figure to indicate they are parallel?) . Line t is the transversal across these two lines. $\angle a$ and $\angle b$ are corresponding angles. Take a tracing paper and trace $\angle a$ on it. Now place this tracing paper over $\angle b$ and see if the angles align exactly. You will observe that the angles match. Check the other corresponding angles in the figure using a protractor. Are all the corresponding angles equal to each other?

In Fig. 5.20, draw a transversal $t$ to the lines $l$ and $m$ such that one pair of corresponding angles is equal. You can measure the angles with a protractor.