Question 6
Draw a pair of lines and a transversal such that they form two distinct angles.
When a line cuts across two other lines, it creates many angles. We will draw this setup. Then we will pick two different angles.
Step 1 — Drawing Lines and a Transversal
We start with two lines. Let us call them Line and Line . These lines can be anywhere. They do not have to be parallel. Next, we draw a third line. This line cuts across Line and Line . We call this third line a transversal. Let us call it Line . The transversal creates points. It crosses Line and Line . At these points, many angles are formed.
Step 2 — Identifying Two Distinct Angles
We need to find two angles. These angles must not be the same. Let us look at the angles formed. At point P, many angles are formed. At point Q, many angles are also formed. We can pick an angle at point P. Let us call it Angle . We can pick another angle at point Q. Let us call it Angle . Angle A and Angle B are distinct angles.
Answer
The diagrams show two lines and a transversal forming two distinct angles, Angle A and Angle B.
More questions in A
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?
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 , and parallel to , and 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 and (what is the notation used in the figure to indicate they are parallel?) . Line t is the transversal across these two lines. and are corresponding angles. Take a tracing paper and trace on it. Now place this tracing paper over 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 to the lines and such that one pair of corresponding angles is equal. You can measure the angles with a protractor.