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# Bisecting Angles

Lesson 4 of 13

## Objective: SWBAT construct an angle bisector using a compass and a straightedge

#### Do Now:

*6 min*

For the Do Now, I have students practice constructing perpendicular bisectors of line segments. As the students walk into the room, I hand them a compass and a straightedge. They then draw three segments of different lengths in their notebooks and bisect each segment. This practice helps students become more comfortable at using a compass and performing constructions.

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#### Mini-Lesson

*15 min*

In the Mini-Lesson, students will learn how to copy a specific angle and how to bisect acute and obtuse angles. I hand out the worksheet "Bisecting Angles Mini-Lesson" and a compass, straightedge, and protractor. Students view the demonstration of "Copying an Angle." I have the students watch the demonstration twice. The first time, they just watch. During the second viewing, the students will try the construction as they watch. After students complete their construction, they use the protractor to verify the two angles have the same measure. We will refer back to the this construction in a later lesson on constructing parallel lines.

We then move on to the second construction, constructing the bisector of the angle. I ask the students to describe what "angle bisector" means. Based on prior knowledge of the word "bisector," students are usually able to describe an angle bisector as a line that divides an angle in two equal parts. I offer an alternative definition of an angle bisector. Although the Common Core standards do not explicitly mention the term "loci," I describe an angle bisector as the locus of points equidistant from both sides of an angle.

We then watch the demonstration showing how to construct the bisector of an angle. Students watch once first and then try the construction as they watch the demonstration a second time. After students finish the construction, I have them measure the two new angles. Before the students work on their own, I have them practice a second time with an obtuse angle.

#### Resources

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#### Activity

*18 min*

During the activity section, students practice copying and bisecting angles. As they work on the sheet, I circulate around the room and help students when necessary. If many students have the same difficulties, I stop the practice and show the students how to bisect the angle again. After each construction, I have the students use a protractor to measure the angles.

As an extension, I have students draw two intersecting lines and practice constructing the bisectors of adjacent angles and vertical angles.

#### Resources

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#### Summary

*6 min*

** **At the end of the lesson, we go over the constructions. We discuss why there may be some slight differences between the two new angles (human error) and how construct the angle bisector more precisely.

**Exit Ticket:** Students construct the bisector of angles formed by intersecting lines. They draw the lines and then perform the construction.

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment

- LESSON 1: What is Geometry?
- LESSON 2: Geometric Terms
- LESSON 3: What are Geometric Constructions?
- LESSON 4: Bisecting Angles
- LESSON 5: Constructing Parallel Lines
- LESSON 6: Constructing Triangles
- LESSON 7: Constructing Inscribed Regular Triangles, Quadrilaterals and Hexagons
- LESSON 8: Introduction to Constructions with Geometer's Sketchpad
- LESSON 9: Constructing Quadrilaterals using Geometer's Sketchpad
- LESSON 10: Constructing Regular Polygons Inscribed in Circles using Geometer's Sketchpad
- LESSON 11: Geometric Construction Review
- LESSON 12: Geometric Constructions End of Unit Assessment
- LESSON 13: Geometric Constructions Assessment Error Analysis