Question 15
Draw two more parallel lines using the long side of the set square as shown in Fig. 5.22. How do you know these two lines are parallel? Can you check if the corresponding angles are equal?
- When a set square slides along a fixed ruler, the inclination angle of its edge relative to the ruler remains constant.
- The straight edge of the ruler acts as a transversal across all drawn lines.
- By the corresponding angles axiom, if the corresponding angles formed with a transversal are equal, the lines must be parallel.
Step 1 · Draw Additional Parallel Lines
To draw two more parallel lines:
- Keep the ruler firmly fixed on the paper in its position.
- Slide the set square along the edge of the ruler to a new position and draw a line along its long side.
- Slide the set square once more along the ruler and draw a second line along the same edge.
Step 2 · Justify Parallelism
- The fixed ruler acts as a transversal line intersecting all the drawn lines.
- As the set square slides along the ruler, the angle between the ruler's edge and the set square's long side remains unchanged.
- Since the corresponding angles made with the transversal are equal, the lines drawn are parallel to line and to each other.
Step 3 · Verify Corresponding Angles
Yes, corresponding angles can be verified:
- Draw any line intersecting all the parallel lines to serve as a transversal.
- Measure the corresponding angles formed at each intersection using a protractor.
- Since each corresponding angle measures the same, the lines are confirmed to be parallel.
- The lines are parallel because the straight edge of the ruler acts as a transversal and all lines make the same angle with it (equal corresponding angles).
- Yes, we can check by drawing a transversal line across them and measuring the corresponding angles with a protractor.
- Shifting the Ruler: Allowing the ruler to move or rotate while sliding the set square changes the angle, causing the resulting lines to not be parallel.
- Misunderstanding the Transversal: Not identifying the straight edge of the ruler as the transversal that creates equal corresponding angles.
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