Using the State Curriculum: Mathematics, Grade 7Algebra  Geometry  Measurement  Statistics  Probability  Number  Processes 
Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teachernot the student. In addition, classroom examples may or may not reflect the assessment limits. 
Standard 2.0 Knowledge of Geometry 
Topic C. Representation of Geometric Figures 
Indicator 1. Represent plane geometric figures 
Objective c. Construct geometric figures using a variety of construction tools 
Clarification 


A perpendicular bisector is a line that intersects a line segment at the midpoint of the segment and forms 90° angles at the point of intersection. An angle bisector is a ray, line segment or line that passes through the vertex of an angle and separates the angle into two congruent angles. Students need to understand the difference between draw and construct. When students draw or sketch a geometric figure, they use rulers and protractors to measure and create the figures. However, for this indicator, students will construct geometric figures, using compass and straightedge, patty paper, or Miras^{TM}. A compass is an instrument used to draw circles and arcs and to duplicate lengths accurately. A straightedge is similar to a ruler but is not used to measure; it is only used to draw a straight line. Patty paper (the name comes from its origin, the paper that is used to separate beef patties) is a square of tracing paper that can be folded and drawn on to demonstrate geometric relationships and duplicate geometric figures. A Mira^{TM} is a transparent and reflective tool that can be used to construct geometric figures through proven geometric relationships. There are several ways that each of these geometric relationships can be modeled. Which way is used in the classroom is determined by the teacher, the available resources, and the needs of the students. It is not expected that students know all of the methods on how to construct perpendicular or angle bisectors. It is to the students' advantage that they be given the opportunity to choose the method most comfortable for them in classroom instruction. The tools available to students on the assessment will be the compass and straightedge. 

Classroom Example 1 

Perpendicular Bisector Steps for students to construct a perpendicular bisector using compass and straightedge:
Look at the figure below. What is the relationship between and line j? Answer: The line segment and the line appear to be perpendicular because the angles formed by them measure approximately 90° What is the relationship between and ? Answer: and appear to be congruent segments because they measure approximately the same length. Point C is the _________________ of . Answer: midpoint Select a point on line j. Label this point X. What is the relationship between and ? Answer: and appear to be congruent because they measure approximately the same length. 

Classroom Example 2 

Steps for students to construct a perpendicular bisector using patty paper:
Look at the figure below. What is the relationship of line k to ? Answer: The line segment and the line appear to be perpendicular because the angles formed by them measure approximately 90° What is the relationship between and ? Answer: and appear to be congruent segments because they measure approximately the same length. Point M is the _________________ of . Answer: midpoint Select a point on line k. Label this point X. What is the relationship between and ? Answer: and appear to be congruent because they measure approximately the same length. 

Classroom Example 3 

Steps for students to construct a perpendicular bisector using Miras^{TM}:
Look at the figure below. What is the relationship of line n to line segment ? Answer: Line n is the perpendicular bisector of line segment 

Classroom Example 4 

Angle Bisector Steps for students to construct an angle bisector using compass and straightedge:
Look at the figure below. What is the relationship between and ? Answer: The angles are congruent. 

Classroom Example 5 

Steps for students to construct an angle bisector using patty paper:
What is the relationship between and ? Answer: The angles are congruent. 

Classroom Example 6 

Steps for students to construct an angle bisector using Miras^{TM}:
Look at the figure below. What is the relationship between and ? Answer: The angles are congruent. Note: Some construction techniques adapted from High School Assessment Core Learning Goal 2 Geometry Instructional Activities, developed in 2003 by the Maryland State Department of Education, accessible at http://www.mdk12.org/instruction/curriculum/hsa/geometry/clg.html 

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