Download Triangle Sum Proof

Triangle Sum Proof
Resource ID#: 60310
Primary Type: Formative Assessment
This document was generated on CPALMS - www.cpalms.org
Students are asked prove that the measures of the interior angles of a triangle sum to 180°.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, proof, triangle sum theorem, triangle interior angle sum, alternate interior
angles
Instructional Component Type(s): Formative Assessment
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_TriangleSumProof_Worksheet.docx
MFAS_TriangleSumProof_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 problem on the Triangle Sum Proof
worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student’s proof shows no evidence of an overall strategy or logical flow.
Examples of Student Work at this Level
The student:

States the given information but is unable to go any further.

Says that three angles of any triangle sum to 180° but provides no justification or reasoning.

The student’s proof does not logically flow and may include unnecessary steps and errors.
Questions Eliciting Thinking
Did you think through a plan for your proof before you started? Did you consider what you already know that m
Why do you think
was added to the diagram? Can you conclude anything from this?
Are there some things you have learned about parallel lines that can help you? If two parallel lines are intersecte
Instructional Implications
Review the meaning of the following: adjacent, straight, supplementary, and alternate interior in the context of p
Alternate Interior Angle Theorem and guide the student to conclude that the alternate interior pairs are congruen
analyze and describe the strategy used in the proof.
If necessary, review notation for naming angles (e.g., < 1) and describing angle measures (e.g., m < 1) and guide
Allow the student to explore the sum of interior angles of triangles using computer software or a graphing calcul
http://www.mathopenref.com/triangleinternalangles.html).
Provide the student with frequent opportunities to make deductions using a variety of previously encountered de




< A and < B are vertical.
< C and < D are corresponding angles (formed by parallel lines intersected by a transversal).
< 1 and < 2 are a linear pair of angles.
is the bisector of < DEF.
Provide the student with additional examples of proofs of statements about triangles and their angles. Ask the stu
Moving Forward
Misconception/Error
The student’s proof reveals some evidence of an overall strategy, but the student fails to establish major conditio
Examples of Student Work at this Level
The student’s proof establishes the congruence of the alternate interior angles but goes no further.
The student’s work states the alternate interior angles are congruent, but then unnecessary steps are included.
Questions Eliciting Thinking
How does knowing the alternate interior angles are congruent help you in this proof?
What do you know by looking at the diagram? Do you see any angle relationships in the diagram other than the
Instructional Implications
Provide proof problems for the student in which the statements and reasons are given separately and the student
If necessary, review notation for naming angles (e.g., < 1) and describing angle measures (e.g., m < 1) and guide
Encourage the student to begin the proof process by developing an overall strategy. Provide another statement to
Consider implementing MFAS task Isosceles Triangle Proof (G-CO.3.10).
Almost There
Misconception/Error
The student’s proof shows evidence of an overall strategy, but the student fails to establish a minor condition tha
Examples of Student Work at this Level
The student fails to state the given in the proof.
The student fails to give a reason for the final statement of the proof.
The student’s proof contains a mistake in the given statement and fails to name the three angles forming the stra
Questions Eliciting Thinking
Does your last step prove that the three angles of the triangle sum to 180°?
There is a slight error in your proof, can you find it?
Look over your proof, did you show appropriate reasons for all of your statements?
Instructional Implications
Provide the student with direct feedback on his or her proof. Prompt the student to supply justifications or statem
If necessary, review notation for naming angles (e.g., < 1) and describing angle measures (e.g., m < 1) and guide
Provide opportunities for the student to determine the flow of a proof. Give the student each step of a proof writt
Consider implementing other MFAS proof tasks, Isosceles Triangle Proof (G-CO.3.10) and Triangle Midsegme
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 presents a convincing proof that alternate interior angles are congruent.
Questions Eliciting Thinking
Could you accomplish this proof without using the Alternate Interior Angles Theorem? How? What other theore
What do you think is the justification for adding
to the diagram? How do we know that there is only one line
Instructional Implications
If necessary, review notation for naming angles (e.g., < 1) and describing angle measures (e.g., m < 1) and guide
Provide the student opportunities to write proofs using a variety of formats some of which include paragraph pro
Consider implementing other MFAS proof tasks, Isosceles Triangle Proof (G-CO.3.10) and Triangle Midsegme
ACCOMMODATIONS & RECOMMENDATIONS

Special Materials Needed:
o
Triangle Sum Proof 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.3.10:
Description
Prove theorems about triangles; use theorems about triangles to
solve problems. Theorems include: measures of interior angles
of a triangle sum to 180°; triangle inequality theorem; base
angles of isosceles triangles are congruent; the segment joining
midpoints of two sides of a triangle is parallel to the third side
and half the length; the medians of a triangle meet at a point.