Download Constructing a Congruent Angle

Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 70620
Constructing a Congruent Angle
Students are asked to construct an angle congruent to a given angle.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, construction, congruent angle
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ConstructingACongruentAngle_Worksheet.docx
MFAS_ConstructingACongruentAngle_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: MAFS.G­CO.4.12 requires students to “make formal geometric constructions with a variety of tools and methods.” This task and rubric assume the use of a compass
and straightedge but can be adapted for use with any tool. Throughout the geometry course, students should be exposed to a variety of construction tools and methods.
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problem on the Constructing a Congruent Angle worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student sketches or draws rather than constructs.
Examples of Student Work at this Level
The student:
Sketches an angle that appears congruent to
.
Uses a protractor to measure and draw a congruent angle.
Uses a compass to measure BC, then constructs two points each a distance of BC from a point E, and draws an angle containing the points.
page 1 of 4 Questions Eliciting Thinking
What is the difference between drawing and constructing?
When doing a geometric construction, what tools are typically used?
What is a disadvantage of using a protractor? Is a compass potentially more accurate?
Instructional Implications
Explain to the student the difference between drawing and constructing. Show the student the tools traditionally used in geometric constructions and explain the purpose
of each. Be sure the student understands that a protractor is not one of the tools used in traditional geometric constructions.
Guide the student through the steps of constructing an angle congruent to a given angle. Have the student label the congruent angle
, as given in the instructions.
Have the student remove any unnecessary marks or marks made in error from his or her paper. Ask the student to write out the steps of the construction and keep them
for future reference. Provide additional opportunities to construct angles in isolation or as part of other constructions such as the construction of a triangle.
Moving Forward
Misconception/Error
The student attempts the construction but makes a significant error.
Examples of Student Work at this Level
The student constructs a working line, marks point E on the working line, and:
With point E as the center, makes an arc congruent to one already drawn on
. The student is unable to complete the construction and simply draws
.
Makes an arc centered at point E with a radius of BC. The student then measures AC with the compass and uses this radius to locate point D.
Questions Eliciting Thinking
You started this construction correctly. How did you determine the radius of this arc?
Are A and C the same distance from B? How can you check this?
How did you determine where to locate
?
Instructional Implications
Explain to the student the need to precisely locate points in constructions, and that points can be precisely located at the intersection of two construction marks. Guide the
student to begin angle constructions with a working line and to use the compass to measure needed lengths.
Guide the student through the steps of constructing an angle congruent to a given angle. Have the student label the congruent angle
, as given in the instructions.
Have the student remove any unnecessary marks or marks made in error from his or her paper. Ask the student to write out the steps of the construction and keep them
for future reference. Provide additional opportunities to construct angles in isolation or as part of other constructions such as the construction of a triangle.
Challenge the student to construct an angle whose measure is the sum of two given angles. Draw the given angles so that they do not share a vertex or side.
Almost There
Misconception/Error
The student correctly completes the construction but does not label the construction or leaves unnecessary marks on the paper.
page 2 of 4 Examples of Student Work at this Level
The student:
Correctly constructs an angle congruent to
Correctly constructs and labels
but does not label it as
. The student may not label the constructed angle at all or labels it as
.
but leaves several unnecessary or unused construction marks on the construction.
Note: The student whose work is shown above also attempted to justify the construction with SAS (rather than SSS).
Questions Eliciting Thinking
Where is
in your construction?
What are these arcs for? Did you use them in your construction?
Instructional Implications
Ask the student to label the congruent angle
, as given in the instructions and to remove any unnecessary marks or marks made in error from his or her paper.
Ask the student to highlight the two triangles formed in the construction and to justify the use of SSS.
Challenge the student to construct angles whose measures are 2(m
),
(m
), and
(m
). Ask the student to appropriately label each constructed angle
and to remove any unnecessary construction marks.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student uses a straightedge to construct a working line. The student marks vertex E on the working line and then uses the SSS method to construct
needed construction marks are shown and no unnecessary marks remain. The student correctly labels the constructed angle as
. All
.
Questions Eliciting Thinking
How can you justify your construction? How do you know that it results in an angle that is congruent to the given one?
Instructional Implications
If the triangle congruence theorems have been introduced, ask the student to write up a justification for the congruent angle construction. Then ask the student to
construct a triangle congruent to a given triangle using the SSS method. Ask the student to explain the similarities in the constructions.
Challenge the student to construct angles whose measures are 2(m
),
(m
), and
(m
). Ask the student to appropriately label each constructed angle
and to remove any unnecessary construction marks.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Compass and straightedge,
Translucent paper,
Reflective devices, or
Dynamic geometry software
Constructing a Congruent Angle worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
page 3 of 4 Related Standards
Name
MAFS.912.G-CO.4.12:
Description
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.
Remarks/Examples:
Geometry - Fluency Recommendations
Fluency with the use of construction tools, physical and computational, helps students draft a model of a geometric
phenomenon and can lead to conjectures and proofs.
page 4 of 4