Parallel and Intersecting Lines | A

Question 8

In Fig. 5.20, draw a transversal tt to the lines ll and mm such that one pair of corresponding angles is equal. You can measure the angles with a protractor.

Question diagram 1
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Solution

We will draw a line that cuts across ll and mm. We will then identify a pair of angles that are in corresponding positions.

Step 1 — Draw the transversal line

We draw a straight line. This line cuts across both line ll and line mm. Let us call this new line tt. This line tt intersects line ll at point A. This line tt also intersects line mm at point B.

Diagram 1

Step 2 — Identify corresponding angles

We need to find a pair of corresponding angles. Corresponding angles are in the same relative position. Let us look at the intersection of line ll and line tt. Let us consider the angle above line ll. This angle is also to the right of line tt. Let us call this angle ∠A1\angle \text{A}_1. Now, let us look at the intersection of line mm and line tt. The angle in the same relative position is above line mm. This angle is also to the right of line tt. Let us call this angle ∠B1\angle \text{B}_1.

Diagram 2

Step 3 — Confirm angle equality

We have identified corresponding angles ∠A1\angle \text{A}_1 and ∠B1\angle \text{B}_1. The problem asks us to draw tt such that these angles are equal. In the given figure, lines ll and mm appear parallel. If lines ll and mm are parallel, corresponding angles are equal. We can use a protractor to measure these angles. We will find that their measures are the same. So, the measure of ∠A1\angle \text{A}_1 is equal to the measure of ∠B1\angle \text{B}_1.

m(∠A1)=m(∠B1)m(\angle \text{A}_1) = m(\angle \text{B}_1)

∠A1=∠B1\boxed{\angle \text{A}_1 = \angle \text{B}_1}

Answer

(i) A transversal line t is drawn intersecting lines l and m. (ii) One pair of corresponding angles, ∠A1\angle \text{A}_1 and ∠B1\angle \text{B}_1, are identified. (iii) These corresponding angles are equal, meaning ∠A1=∠B1\angle \text{A}_1 = \angle \text{B}_1.

More questions in A

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?

Q2

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.

Q3

What patterns do you observe among these angles?

Q4

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?
Q5

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 aa, bb and cc parallel to pp, qq and rr respectively? Why or why not?
Q6

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

Q7

Fig. 5.19 has a pair of parallel lines ll and mm (what is the notation used in the figure to indicate they are parallel?) . Line t is the transversal across these two lines. ∠a\angle a and ∠b\angle b are corresponding angles. Take a tracing paper and trace ∠a\angle a on it. Now place this tracing paper over ∠b\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?

Q8

In Fig. 5.20, draw a transversal tt to the lines ll and mm such that one pair of corresponding angles is equal. You can measure the angles with a protractor.

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