Question

gerald is constructing a line parallel to line l through point p. he begins by drawing line m through points p and q. he then draws a circle centered at q, which intersects line l at point n and line m at point s. keeping the compass measure, he draws a congruent circle centered at point p, which intersects line m at point t. which next step will create point r, such that when a line is drawn through points p and r, the line will be parallel to line l?

Explanation:

Step1: Recall parallel - line construction principle

When constructing a parallel line, we use the property of congruent corresponding angles.

Step2: Identify key lengths

The distance between N and S on the circle centered at Q represents a key length related to the angle formed by line \(l\) and line \(m\).

Step3: Replicate the length at point P

By setting the compass width to the distance between N and S and placing the compass at T on the circle centered at P, we are creating a congruent angle - related construction. The intersection of the arc and the circle centered at P gives us point R. When a line is drawn through P and R, it will be parallel to line \(l\) due to the congruence of corresponding angles formed in the construction.

Answer:

Set the compass width to the distance between N and S, place the compass at T, and draw an arc that intersects the circle centered at P. The intersection point is R.