Question

b) explain how you could use the construction tool or a compass and straightedge to create a line segment that is twice as long as $\overline{ab}$. a b

Explanation:

Step1: Draw a ray

Use the straight - edge to draw a ray \( CD\).

Step2: Set the compass width

Open the compass to the length of \( \overline{AB}\).

Step3: Mark the first segment

With the compass, mark a segment \( CE\) on ray \( CD\) such that \( CE = AB\) (place the compass at \( C\) and draw an arc intersecting the ray at \( E\)).

Step4: Mark the second segment

Without changing the compass width (still set to the length of \( AB\)), place the compass at \( E\) and draw an arc intersecting the ray \( CD\) at a point \( F\).

Answer:

The line segment \( CF\) is twice as long as \( \overline{AB}\) since \( CF=CE + EF\) and \( CE = AB\), \( EF = AB\).