The purpose of this activity is to extend what students know about constructing a perpendicular line through a point on the given line to a new situation in which the constructed perpendicular line goes through a point not on the given line.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

Focus on the process of using a previous construction to generate new constructions. Here are some questions for discussion:

• “How was this construction different from perpendicular line constructions you have done before? How did thinking about the differences help you plan what to do?” (I didn't have a segment to bisect because the point wasn't on the line. I realized I could still make a segment using the new point.)
• “How does knowing some constructions help you do other, more complicated constructions?” (I can use the same moves, but just change them a little bit.)

The purpose of this activity is for students to think strategically about how to apply previous constructions to a new construction.

It is not expected that students will use any method other than two consecutive perpendicular lines, but if students come up with other methods, consider discussing those methods during the Lesson Synthesis.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

The purpose of the discussion is to focus on the process of using previous constructions to generate new constructions. Ask students, “How does knowing some constructions help you do other, more complicated constructions?” (In this construction, I repeated a construction I already knew twice.)

Add an additional item to the display of constructions students already know:

• A parallel line through a point not on the given line

Some students may struggle more than is productive. Ask these students to draw a line segment and construct the perpendicular bisector of it. In that construction, the perpendicular bisector will go through an intersection point of two circles. Ask, “What happens if you create a circle centered at that intersection point that goes through an endpoint of the segment? Why does that happen? How can you use this idea in this new activity?”

Some students may struggle more than is productive. Ask these students to consider what they just learned to construct starting from the point and line. (A perpendicular line.) Invite them to consider the relationship between the line they could construct and the parallel line they want to construct. (Those are also perpendicular.)