Question

try it! copy a segment

1. how can you construct a copy of $overline{xy}$?

image of segment $overline{xy}$ with endpoints x (left) and y (right)

Explanation:

Step1: Draw a ray

Draw a ray (let's call its endpoint \( A \)) that will be the base for the copied segment. This ray should be long enough to accommodate the length of \( \overline{XY} \).

Step2: Measure \( \overline{XY} \)

Use a compass to measure the length of \( \overline{XY} \). Place the compass point on \( X \) and adjust the compass width so that the pencil point is on \( Y \).

Step3: Mark the length on the ray

Without changing the compass width, place the compass point on \( A \) (the endpoint of the ray) and draw an arc that intersects the ray. Let the intersection point be \( B \). Now, \( \overline{AB} \) is a copy of \( \overline{XY} \) because \( AB = XY \) (by the way we set the compass width).

Answer:

To construct a copy of \( \overline{XY} \):

1. Draw a ray with endpoint \( A \).
2. Use a compass to measure the length of \( \overline{XY} \) (place compass on \( X \), pencil on \( Y \)).
3. With the compass width unchanged, place the compass on \( A \) and draw an arc intersecting the ray at \( B \). \( \overline{AB} \) is the copy of \( \overline{XY} \).