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After quiet work time, ask students to compare their responses to their partner’s and decide whether they are both correct, even if they are different.
Here is a line and a point not on the line. Use straightedge and compass moves to construct a line perpendicular to line that goes through point . Be prepared to share your reasoning.
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?”
Focus on the process of using a previous construction to generate new constructions. Here are some questions for discussion:
Add an additional item to the display of different constructions that students have learned:
Remind students that they can use their catalog to think about how to use constructions they know to build something new.
Ask students what it means for lines to be parallel. (They never intersect.)
Here is a line and a point not on the line. Use straightedge and compass moves to construct a line parallel to line that goes through point .
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.)
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: