Constructions, Proof, and Rigid Motion

Lesson 4

Math

Unit 1

10th Grade

Lesson 4 of 19

Objective


Construct a perpendicular bisector.

Common Core Standards


Core Standards

  • G.CO.A.1 — Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
  • G.CO.D.12 — Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Criteria for Success


  1. Construct a perpendicular line segment and make connections of the steps of this construction to other constructions you already know how to do.
  2. Partition a line segment into (products of two) equal parts using a series of perpendicular bisectors.

Tips for Teachers


This lesson directly builds off the last lesson in the unit.

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Anchor Problems

25-30 minutes


Problem 1

Bisect the following angle using constructions. Point $$A$$ should be considered the vertex of the angle.

$$\overline{CA}\cong \overline{AB}$$

 

 

Guiding Questions

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Problem 2

Construct a perpendicular bisector for the following line segment. Write the steps of construction.

 

Guiding Questions

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Target Task

5-10 minutes


 

  • Label the point of intersection of the perpendicular bisector that bisects $${{AB}}$$ and the line segment $${{AB}}$$ with the letter $$C$$.
  • Choose a point on this perpendicular bisector and label this $$D$$.
  • What is the relationship between $$\overline{AD}$$ and $$\overline{BD}$$? What is the angle measure of $$\angle DCB$$?

References

EngageNY Mathematics Geometry > Module 1 > Topic A > Lesson 4Exit Ticket

Geometry > Module 1 > Topic A > Lesson 4 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems that give students line segments and have them name points that are not collinear to the endpoints of the segment but are equidistant from the endpoints of the line segment.
  • Include problems that ask students to justify their reasoning. For example: “Is point _____ equidistant from the endpoints of the line segment? How would you figure that out only using a compass? This is a really important question!”
  • Make sure to give students lots of practice that leads them to partitioning into equal lengths. This is a natural extension of the perpendicular bisector.

Next

Construct the altitudes and perpendicular bisectors of sides of triangles.

Lesson 5
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Constructions of Basic Geometric Figures

Topic B: Justification and Proof of Angle Measure

Topic C: Translations of Points, Line Segments, and Angles, and Parallel Line Relationships

Topic D: Reflections and Rotations of Points, Line Segments, and Angles

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