Download Export To Word

Congruence Implies Congruent
Corresponding Parts
Resource ID#: 59703
Primary Type: Formative Assessment
This document was generated on CPALMS - www.cpalms.org
Students are given two congruent triangles and asked to determine the corresponding side
lengths and angle measures and to use the definition of congruence in terms of rigid motion to
justify their reasoning.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, congruence, congruent pairs, triangle, transformation, rigid motion,
translation, rotation, reflection
Instructional Component Type(s): Formative Assessment
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_CongruenceImpliesCongruentCorrespondingParts_Worksheet.pdf
MFAS_CongruenceImpliesCongruentCorrespondingParts_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with a small group, or with the whole class.
1. The teacher asks the student to complete the problems on the Congruence Implies
Congruent Corresponding Parts worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
Given a congruence statement, the student is unable to identify corresponding sides and/or angles.
Examples of Student Work at this Level
The student writes something like:


.
DF = 4.
Questions Eliciting Thinking
Can you explain how you determined your answers?
If you were not shown the triangles, how could you determine which vertices correspond from the congruence st
What are corresponding sides and angles? Can you identify the corresponding sides and angles of the two congr
Instructional Implications
Explain to the student that the congruence statement reflects the correspondence between the vertices of the two
statement to determine the six pairs of corresponding parts and how to write the six congruence statements that r
corresponding parts are marked congruent. Ask the student to write a congruence statement for each.
Address issues with the use of the definition of congruence in terms of rigid motion to justify the congruence of
Moving Forward
Misconception/Error
The student does not understand that the congruence ensures there is a sequence of rigid motions that will map o
Examples of Student Work at this Level
After identifying the lengths of the sides and measures of the angles of
, the student attempts to describe a
Questions Eliciting Thinking
What is the definition of congruence in terms of rigid motion?
If two triangles are congruent, what does the definition tell you must be true?
Instructional Implications
Explain to the student that this task is a part of the proof of the statement, "Two triangles are congruent if and on
form "p if and only if q," there are actually two statements that must be established: "If p then q," and "If q then
pairs of angles are congruent," one must prove both of the following: "If two triangles are congruent, then corres
and corresponding pairs of angles are congruent, then the two triangles are congruent." The problem in this task
Review the definition of congruence in terms of rigid motion and explain to the student that the congruence of th
identify the sequence. Review the basic properties of rigid motion, [i.e., (1) rigid motions map lines to lines, ray
the student in understanding that since ABC
DEF, there is a sequence of rigid motions that maps
and
, so the corresponding parts of the congruent triangles are congruent.
ABC
Allow the student ample time to explore how sequences of rigid motions ensure congruence by using manipulati
http://nlvm.usu.edu/en/nav/frames_asid_294_g_4_t_3.html?open=activities&from=category_g_4_t_3.html). Ha
another. Ask the student to describe how the basic properties of rigid motion are demonstrated in this activity. M
the preimage and image are congruent.
Be sure to address any issues with the misuse of notation (e.g., writing
= 6 rather than DE = 6 or
rath
Consider implementing MFAS task Showing Congruence Using Corresponding Parts - 1 (G-CO.2.7) which add
congruent, then the two triangles are congruent."
Almost There
Misconception/Error
The student is unable to generalize from the example to all triangles.
Examples of Student Work at this Level
The student is unable to clearly explain how the reasoning used in question 2 can be applied to any pair of triang
Questions Eliciting Thinking
If I changed the way these two triangles look or are oriented on the paper, how could you determine the correspo
How could you apply your reasoning in this example to any pair of triangles?
Instructional Implications
Explain to the student that there is nothing about the reasoning used to conclude
,
,
,
triangles given in the diagram and ask the student to complete questions 1 and 2 again. Then ask the student to c
Be sure to address any issues with the misuse of notation (e.g., writing
= 6 rather than DE = 6 or
rath
Consider implementing MFAS task Showing Congruence Using Corresponding Parts - 1 (G-CO.2.7) which add
congruent, then the two triangles are congruent."
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 determines the lengths of the sides of
DEF are DE = 6, DF = 5, and EF = 4, and the measures of t
of rigid motions that maps ABC onto DEF. Since rigid motions preserve both distance and angle measure, th
that is specific to ABC and DEF; this reasoning can be applied to any pair of triangles. So, if two triangles a
Questions Eliciting Thinking
You showed that if two triangles are congruent, then corresponding pairs of sides and corresponding pairs of ang
Instructional Implications
Consider implementing MFAS task Showing Congruence Using Corresponding Parts - 1 (G-CO.2.7) which add
congruent, then the two triangles are congruent."
ACCOMMODATIONS & RECOMMENDATIONS

Special Materials Needed:
o
Congruence Implies Congruent Corresponding Parts 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.912.G-CO.2.7:
Description
Use the definition of congruence in terms of rigid motions to
show that two triangles are congruent if and only if
corresponding pairs of sides and corresponding pairs of angles
are congruent.