Question

elliot is constructing a line parallel to a given line l through a point p, which is not on line l. his construction is shown below. what is the next step to correctly complete the construction? draw an arc with a radius equal to df centered at g. draw an arc with a radius equal to de centered at g. draw an arc with a radius equal to ef centered at g. draw an arc with a radius equal to ef centered at p.

Explanation:

Step1: Analyze parallel - line construction principle

To construct a line parallel to a given line through a point, we use the property of equal corresponding angles. Here, we first create an angle at the given point equal to an angle on the given line. After creating an initial arc at point \(P\) and some arcs on line \(l\), the next step is to copy the length that determines the angle - measure on line \(l\) to the point \(P\)'s side.

Step2: Identify the key length

The length \(EF\) is used to determine the angle - measure on line \(l\). We need to draw an arc with a radius equal to \(EF\) centered at \(G\) (the intersection of the first arc drawn from \(P\) and the line passing through \(P\) and intersecting the construction related to line \(l\)) to create an equal - angle situation for parallel - line construction.

Answer:

Draw an arc with a radius equal to \(EF\) centered at \(G\).