This activity invites students to play with straightedge and compass moves to construct a line perpendicular to a given line through a point on the given line. 

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

The goal of this discussion is to establish a method for constructing a perpendicular line. Ask 2 or 3 students to explain how they were able to construct a perpendicular line. Connect these methods with the figure students explored in the Warm-up (two circles where each center is on the other circle).

In this activity, students take turns using a straightedge and compass to construct an angle bisector. Students trade roles, explaining their thinking and listening, providing opportunities to explain their reasoning and critique the reasoning of others (MP3).

This is the first time Math Language Routine 3: Critique, Correct, Clarify is suggested in this course. In this routine, students are given a “first draft” statement or response to a question that is intentionally unclear, incorrect, or incomplete. Students analyze and improve the written work by first identifying what parts of the writing need clarification, correction, or details, then writing a second draft (individually or in pairs). Finally, the teacher scribes as a selected second draft is read aloud by its author(s), and the whole class is invited to help edit this “third draft” by clarifying meaning and adding details to make the writing as convincing as possible to everyone in the room. Typical prompts are “Is anything unclear?” and “Are there any reasoning errors?” The purpose of this routine is to engage students in analyzing mathematical writing and reasoning that is not their own and to solidify their knowledge and use of language.

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

The purpose of this discussion is to connect the previous construction of a perpendicular line with the construction of an angle bisector.

Use Critique, Correct, Clarify to give students an opportunity to improve a sample written response by correcting errors, clarifying meaning, and adding details. 

• Display this first draft: “I made three circles, and then I drew a line through the middle.”
  Ask, “What parts of this response are unclear, incorrect, or incomplete?,” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft. 
• Select 1–2 individuals or pairs to read their revised draft aloud slowly enough to record for all to see. Scribe as each student shares, then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.

Introduce the term angle bisector. Tell students that bi means “two” and sect means “cut,” so bisecting an angle literally means to cut the angle into two congruent angles.

Some students may get stuck for longer than is productive. Ask these students to think about how they could use their tools to construct points and like in the Warm-up.

Some students may get stuck for longer than is productive. Ask these students how they could use their tools to construct a segment they know how to cut in half like they did in the warm-up and in the last activity. If they need further help, ask them to construct a circle centered at , and highlight the segment created when connecting the two intersection points.