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
Understand the Question
  • A transversal is a line that intersects two or more lines at distinct points.
  • When a transversal intersects two parallel lines, corresponding angles (angles in the same relative position at each intersection) are equal.
  • Drawing a transversal line tt intersecting lines ll and mm creates pairs of corresponding angles whose measures can be verified with a protractor.

Step 1 · Draw the Transversal Line

Draw a straight line tt that cuts across both lines ll and mm, intersecting line ll at point AA and line mm at point BB.Diagram 1

Step 2 · Identify a Pair of Corresponding Angles

Corresponding angles lie in the same relative position at each intersection:

  • At intersection AA, choose the angle above line ll and to the right of line tt, labeled ∠A1\angle A_1.
  • At intersection BB, choose the angle above line mm and to the right of line tt, labeled ∠B1\angle B_1.Diagram 2

Step 3 · Verify Equality Using a Protractor

Since lines ll and mm are parallel, measuring with a protractor confirms:

m(∠A1)=m(∠B1)m(\angle A_1) = m(\angle B_1)

∠A1=∠B1\angle A_1 = \angle B_1

Answer

A transversal tt is drawn intersecting lines ll and mm such that corresponding angles are equal, ∠A1=∠B1\angle A_1 = \angle B_1.

Common Mistakes
  • Confusing Angle Pairs: Picking alternate interior angles (Z-shape) or vertically opposite angles (X-shape) instead of corresponding angles (F-shape in the same relative position).
  • Incorrect Relative Positions: Pairing an angle in the top-right position at one intersection with an angle in the bottom-left position at the other.

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 tt 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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