Download Justifying Angle Relationships

Justifying Angle Relationships
Resource ID#: 70163
Primary Type: Formative Assessment
This document was generated on CPALMS - www.cpalms.org
Students are asked to describe and justify the relationship between corresponding angles and
alternate interior angles.
Subject(s): Mathematics
Grade Level(s): 8
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, angle, supplementary, informal justification, transversal, corresponding
angles, alternate interior angles
Instructional Component Type(s): Formative Assessment
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_JustifyingAngleRelationships_Worksheet.docx
MFAS_JustifyingAngleRelationships_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Justifying Angle
Relationships worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to describe the relationship between the measures of the angles.
Examples of Student Work at this Level
The student may correctly identify the angle pairs as alternate interior and corresponding but is unable to describ
Questions Eliciting Thinking
What do you know about the measures of these angles?
Is it important that the lines are parallel?
What do you know about the measures of any angle pair in the diagram?
Instructional Implications
Review the definitions of straight angle, linear pair of angles, supplementary angles, vertical angles, and transve
intersected by a transversal. Provide diagrams of two lines intersected by a transversal (some of which include tw
linear pairs of angles, corresponding angles, alternate interior angles, and same-side interior angles. Give the stu
Allow the student to explore the relationships among the measures of angles formed by two lines and a transvers
transversal and an example of two parallel lines intersected by a transversal. Ask the student to trace angles and
to observe that when the lines are parallel, corresponding angles are congruent. Encourage the student to explore
stating, when two parallel lines are intersected by a transversal:



Corresponding angles are congruent.
Alternate interior angles are congruent.
Same-side interior angles are supplementary.
Provide a diagram of two parallel lines intersected by a transversal with one angle measure indicated. Ask the st
Consider implementing the CPALMS Lesson Plan Special Angle Pairs Discovery Activity (ID 26664), a lesson w
by a transversal, or the CPALMS Lesson Plan An Investigation of Angle Relationships Formed by Parallel Line
Making Progress
Misconception/Error
The student is unable to clearly justify the relationship between the measures of the angles.
Examples of Student Work at this Level
The student states that the angles in each angle pair have the same measure (or are congruent). However, the stu
Questions Eliciting Thinking
How did you determine the angles are equal?
Do you know the names of any of the special angle pairs in the diagram?
Instructional Implications
Ask the student to explain how he or she determined that the angle measures are congruent. Assist the student in
example, if the student used tracing paper to copy one angle and compare it to the other angle, help the student d
congruence of the angles.
Provide additional opportunities to justify the relationship between the measures of angles formed by parallel lin
developing a logical argument.
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 states that the angles in each angle pair are the same measure (or are congruent) and provides an app


Traces one of the angles and places it on top of the other angle so that the vertex and both sides of the on
Logically reasons that vertical angles are congruent, and when two parallel lines are intersected by a tran
is congruent to since they are vertical and is congruent to since they are alternate interior (or s
congruent to .
Questions Eliciting Thinking
You used tracing paper to copy one angle and compare it to the other. What rigid motion might describe what yo
Do you know the name of this kind of angle pair?
Would the measures of
and
(or
and
) still be equal if lines m and n were not parallel?
Instructional Implications
If the student used a tracing paper demonstration to explain the relationship between the angle measures:


Ask the student to describe a rigid motion that maps one angle onto the other.
Review previously established angle relationships such as: (1) vertical angles are congruent, and (2) whe
congruent. Then ask the student to logically reason about the relationship between the angle measures.
Consider implementing other MFAS tasks from standard 8.G.1.5 to further explore the student’s understanding o
ACCOMMODATIONS & RECOMMENDATIONS

Special Materials Needed:
o
Justifying Angle Relationships 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
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.8.G.1.5:
Description
Use informal arguments to establish facts about the angle sum
and exterior angle of triangles, about the angles created when
parallel lines are cut by a transversal, and the angle-angle
criterion for similarity of triangles. For example, arrange three
copies of the same triangle so that the sum of the three angles
appears to form a line, and give an argument in terms of
transversals why this is so.