Download The Measure of an Angle of a Triangle

Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 123110
The Measure of an Angle of a Triangle
Students are given the measure of one interior angle of an isosceles triangle and are asked to find the measure of another interior angle.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Keywords: MFAS, interior angle, isosceles triangle, measure
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_TheMeasure OfAnAngleOfATriangle_Worksheet.docx
MFAS_TheMeasure OfAnAngleOfATriangle_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 Measure of an Angle of a Triangle worksheet.
2. The teacher asks follow-up questions, as needed.
Note: In the rubric, the following theorems are referenced by name:
Isosceles Triangle Theorem – In a triangle, angles opposite congruent sides are congruent.
Triangle Sum Theorem – The sum of the measures of the three angles of a triangle is 180°.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to correctly apply relevant theorems to find the missing angle measures.
Examples of Student Work at this Level
The student understands the need to apply the Triangle Sum Theorem but:
Applies the theorem incorrectly.
page 1 of 4 Subtracts 35 from 180 and then is unable to continue.
Makes a false assumption such as the triangle is right.
Questions Eliciting Thinking
What does the Triangle Sum Theorem say? What do the measures of the angles of a triangle sum to?
What is the significance of
? Did you use this fact in your solution?
Can you explain why you think this triangle is a right triangle?
Instructional Implications
Review the Isosceles Triangle Theorem and the Triangle Sum Theorem. Explain the relevance of these theorems to the given problem. Guide the student to apply each
theorem to find the missing angle measure. Then show the student a model solution, such as:
Since
, then
Therefore,
(by the Isosceles Triangle Theorem). Let
. Then 2x + 35 = 180° (by the Triangle Sum Theorem) so that x = 72.5°.
.
Explain each step of the solution, and establish conventions for justifying work (e.g., citing a supporting definition, postulate, or theorem in parentheses near the statement
it justifies).
Review other theorems related to triangles (e.g., The measures of the acute angles of a right triangle sum to 90°, or the measure of each angle of an equilateral triangle is
60°.). Then provide opportunities to find missing angle measures in isosceles, right, and equilateral triangles. Ask the student to justify his or her work.
If needed, assist the student in using notation correctly. Be sure the student understands how to correctly write both equations (e.g.,
statements (e.g.,
) and congruence
).
Moving Forward
Misconception/Error
The student can find the missing angle measure but is unable to adequately justify his or her answers.
Examples of Student Work at this Level
The student correctly determines that the measure of
is 72.5°. However, the student’s justification is incorrect or incomplete. For example, the student:
Fails to cite the Triangle Sum Theorem.
Fails to cite the Isosceles Triangle Theorem.
page 2 of 4 Describes the computations used without providing justification.
Questions Eliciting Thinking
How do you know to subtract 35 from 180?
How do you know
and
are congruent? What supports this statement?
What does it mean to justify your work? What postulates or theorems have you used in finding this angle measure?
Instructional Implications
Explain that a complete justification includes any relevant definitions, postulates, or theorems that support conclusions drawn about angle measures or equations written to
model angle relationships. Provide feedback to the student concerning any error or omission in his or her justification. Assist the student in identifying and citing the relevant
theorems.
Encourage the student to write and solve an equation to find the missing angle measure. Show the student a model solution, such as:
Since
, then
(by the Isosceles Triangle Theorem). Let
Therefore,
. Then 2x + 35 = 180° (by the Triangle Sum Theorem) so that x = 72.5°.
.
Provide additional opportunities for the student to find missing angle measures in triangles and to justify his or her work.
Almost There
Misconception/Error
The student’s solution contains notational errors, a misuse of terminology, or incorrectly written mathematics.
Examples of Student Work at this Level
The student correctly determines that the measure of
is 72.5° and justifies the solution by citing both the Triangle Sum Theorem and the Isosceles Triangle Theorem.
However, the student makes notational errors, misuses terminology, or incorrectly writes mathematical work.
Questions Eliciting Thinking
What are the two congruent angles of an isosceles triangle called? What is the third angle of an isosceles triangle called?
You made some notational errors when you wrote up your work. Can you find and correct them?
Can you find the error in this equation,
?
Instructional Implications
If needed, review terminology used to describe the parts of an isosceles triangle (i.e., base, legs, base angles, and vertex angle). Provide feedback to the student
concerning any notational errors or incorrectly written mathematics, and allow the student to revise his or her solution.
Encourage the student to write and solve an equation to find the missing angle measure. Show the student a model solution, such as:
Since
, then
Therefore,
(by the Isosceles Triangle Theorem). Let
. Then 2x + 35 = 180° (by the Triangle Sum Theorem) so that x = 72.5°.
.
Provide additional opportunities for the student to find missing angle measures in diagrams and to justify his or her work.
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 correctly determines that the measure of
is 72.5° and justifies the solution by citing both the Triangle Sum Theorem and the Isosceles Triangle Theorem.
page 3 of 4 Questions Eliciting Thinking
How do you know the triangle is isosceles?
How would you find the measure of
if the measure of
had been given as
?
Instructional Implications
If the student did not do so, ask the student to write and solve an equation to find the missing angle measure.
If not done previously, ask the student to prove the Triangle Sum Theorem and the Isosceles Triangle Theorem.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
The Measure of an Angle of a Triangle worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Access Privileges: Public
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.
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