Question

1. construct a line parallel to line ab through point y.

Explanation:

Step1: Draw a transversal line

Draw a line from point \( Y \) that intersects line \( AB \). Let's call the intersection point \( C \).

Step2: Copy the angle

Using a compass, measure the angle at \( C \) between line \( AB \) and the transversal. Then, with the compass still set to that width, place the compass at point \( Y \) and draw an arc that intersects the transversal.

Step3: Draw the parallel line

Using a straightedge, draw a line through point \( Y \) that makes the same angle with the transversal as the angle at \( C \) on line \( AB \). This new line is parallel to line \( AB \).

Answer:

A line parallel to \( AB \) through \( Y \) is constructed as described above.