Bisector Bonanza

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SWBAT construct the bisector of a segment or the bisector of an angle. Students will understand the meaning of a bisector in terms of congruent segments and angles.

Big Idea

Students use compass and straight-edge, aided by tracing paper and paper-folding, to explore the properties of bisectors, while gaining insights into the workings of transformations.

Lesson Open

9 minutes

The warm-up prompt for this lesson asks students to recall the steps in the construction of the bisector of two points.   I display the prompt using the slide show for the lesson.

The purpose of the warm-up is to help students make a connection to prior knowledge.  I want students to see the similarity between the construction of angle bisectors and segment bisectors and the construction of the bisector of two points, whose properties they studied in the first unit (MP7).  This will help them to understand and remember the new constructions better.  It will also help them to realize that the construction of an angle bisector, the construction of a segment bisector, and--in the next lesson--the construction of a perpendicular, are all based on properties of a bisector.  In the next unit, we will prove the properties of bisectors formally, and see that they are very useful in transformation proof.

The warm-up follows our Team Warm-up routine.  I choose students at random to write the team's answer on the board.  

Following the warm-up, I display the Agenda and Learning Targets for the lesson.  I tell the class that we will be learning two new constructions...but if students pay close attention they will see that there is little that is new about these constructions at all.



Introducing Angle and Segment Bisectors

15 minutes

I use the guided notes to introduce the class to angle bisectors and segment bisectors. Then, I demonstrate the construction of each bisector.  Students follow along while completing the constructions right in their notes.

More on how I use guided notes to teach constructions can be found in my lesson, Introduction to Constructions.

Practicing Constructions

25 minutes

During this part of the lesson, students complete two practice activities.  One focuses on the construction of angle bisectors, the other on the construction of segment bisectors. The two exercises flow together.  I manage which problems to hand out to ensure that all students are at least mastering the basic constructions.  

I display the instructions as I distribute the first problem and students get down to work.  The activity uses the Rally Coach format, so that students may provide each other support and check each other's work.

In addition to providing practice in constructions, the exercises ask students to verify the properties of the bisectors in terms of congruent segments and angles.  I encourage and coach them in verifying congruence with construction techniques, using tracing paper, or by trying paper folding strategies (MP5).

The exercises also provide opportunities to see whether students are performing the constructions accurately and labeling the figures correctly (MP6).

The second provides opportunities to challenge students who move quickly.  I look for opportunities to make connections by noticing the structure of the constructions (MP7) and to reason about the properties of the bisectors of the sides of a triangle (MP3). 


Lesson Close and Homework

5 minutes

Individual Size-Up

Displaying the Lesson Close prompt, I ask students to tell how the constructions of segment bisectors and angle bisectors are similar to the construction of the bisector of two points.  This activity follows our Individual Size-Up Routine.



Homework Set 1 problems #15 and 16 provide additional practice in the constructions of angle and segment bisectors which students learned in the lesson.  Problem #17 asks students to describe the symmetry of a number of regular polygons, helping students maintain skills learned in prior lessons.