To draw a line segment parallel to a given line segment $PQ$ using a set square and ruler, follow these steps:

Materials needed:

• Set square (right-angled triangle ruler)
• Straight ruler
• Pencil

Steps:

1. Place the ruler along line segment $PQ$:

   • Align the edge of the ruler so that it runs exactly along the line segment $PQ$.

2. Position the set square against the ruler:

   • Place one of the edges of the set square (not the hypotenuse) against the ruler. Make sure the set square is touching the ruler firmly.

3. Slide the set square along the ruler:

   • Without moving the ruler, slide the set square along its edge until it reaches the position where you want to draw the new parallel line. Ensure the set square stays straight as you move it.

4. Draw the new line:

   • Once the set square reaches the desired position, use the straight edge of the set square to draw a new line segment. This line will be parallel to the original $PQ$.

5. Check alignment:

   • To confirm the line is parallel, you can use a protractor or simply verify that the distance between the two lines is constant.

Would you like more details or have any questions?

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Here are five related questions for further learning:

1. How can you verify two lines are parallel using geometry principles?
2. What are the properties of parallel lines in Euclidean geometry?
3. How would you draw a perpendicular line to $PQ$ using the same tools?
4. Can parallel lines intersect in non-Euclidean geometry?
5. What is the difference between skew lines and parallel lines?

Tip: When drawing lines, ensure your set square doesn't move while sliding along the ruler to maintain accuracy.