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Justifying the Exterior Angle of a Triangle Theorem Resource ID#: 70182 Primary Type: Formative Assessment This document was generated on CPALMS - www.cpalms.org Students are asked to apply the Exterior Angle of a Triangle Theorem and provide an informal justification. Subject(s): Mathematics Grade Level(s): 8 Intended Audience: Educators Freely Available: Yes Keywords: MFAS, angle, interior, exterior, adjacent, non-adjacent, supplementary, informal justification Instructional Component Type(s): Formative Assessment Resource Collection: MFAS Formative Assessments ATTACHMENTS MFAS_JustifyingTheExteriorAngleOfATriangleTheorem_Worksheet.docx MFAS_JustifyingTheExteriorAngleOfATriangleTheorem_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 the Exterior Angle of a Triangle Theorem worksheet. 2. The teacher asks follow-up questions, as needed. TASK RUBRIC Getting Started Misconception/Error The student is unable to draw an exterior angle of a triangle. Examples of Student Work at this Level The student: Creates a new angle at vertex B. Labels the interior angle at vertex B as the exterior angle. Provides no answer or indicates he or she does not understand. Questions Eliciting Thinking What is meant by an interior angle of a triangle? Can you show me an example of an interior angle? What is an exterior angle of a triangle? Can you draw an example? If I extend (demonstrate for the student), which angle is the exterior angle? Instructional Implications Review the following terms: interior angle of a triangle, exterior angle of a triangle, nonadjacent (or remote) inte Show the student that there are two exterior angles at each vertex formed by extending all sides of the triangle at is vertical and, therefore, congruent and that the interior and exterior angle at each vertex form a linear pair. Prov vertex. Guide the student in translating the statement of the Exterior Angle Theorem into a specific statement (e.g., equa drawn and ask the student to write equations that show the relationship between the measure of each exterior ang Assist the student in developing an informal justification of the Exterior Angle Theorem using tracing paper. Th of angles is supplementary and (2) the measures of the interior angles of a triangle sum to 180°. Then guide the s Moving Forward Misconception/Error The student is unable to apply the Exterior Angle Theorem to write an equation. Examples of Student Work at this Level The student is able to extend student: and identify the exterior angle formed as Writes an equation in which sides are set equal to angles. . However, the student is unable to a References an angle or a side but does not write an equation. Writes an incorrect equation. Questions Eliciting Thinking Can you show me the location of each angle in your equation? Is it true that the sum of the measures of the three What does the Exterior Angle Theorem state? Does your equation model this? Show me how you would write the sum of the measures of and . According to the theorem, what does the Instructional Implications Review the following terms: interior angle of a triangle, exterior angle of a triangle, nonadjacent (or remote) inte student in translating the statement of the theorem into a specific statement (e.g., equation) about the given diagr to write equations that show the relationship between the measure of each exterior angle and its two nonadjacent Assist the student in developing an informal justification of the Exterior Angle Theorem using tracing paper. Th of angles is supplementary and (2) the measures of the interior angles of a triangle sum to 180°. Then guide the s Review how to name angles and sides and how to refer to their measures and lengths. Provide feedback to the st Almost There Misconception/Error The student is unable to provide a clear justification for the theorem. Examples of Student Work at this Level The student: Provides an example rather than a justification. Provides a statement, whether true or not, that does not justify the theorem. (e.g., "The angles of a triangl Provides insufficient justification. Questions Eliciting Thinking What do you know about the relationship between an exterior angle and its adjacent interior angle? What do you know about the sum of the measures of the interior angles of a triangle? Instructional Implications Assist the student in developing an informal justification of the Exterior Angle Theorem using tracing paper. Th of angles is supplementary and (2) the measures of the interior angles of a triangle sum to 180°. Then guide the s Review how to name angles and sides, and how to refer to their measures and lengths. Provide feedback to the s Provide additional opportunities to justify the relationship between the measures of angles. Assist the student in 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 extends and identifies the exterior angle formed as . The student writes the equation Traces and , then redraws them so they share a vertex and a side. Then the student uses tracing pap Explains that and are supplementary (or = 180°) since they form a linear pair. The stu angles of any triangle sum to 180°). The student then reasons that so Questions Eliciting Thinking What other angle relationships could you identify if you draw a line parallel to through point C and consider Instructional Implications If the student used a demonstration using tracing paper to justify the Exterior Angle Theorem, review previously supplementary and (2) the measures of the interior angles of a triangle sum to 180°. Then ask the student to logic Ask the student to draw a line through point C parallel to and reason about the angle relationships formed by Consider implementing other 8.G.1.5 tasks to further assess the student. ACCOMMODATIONS & RECOMMENDATIONS Special Materials Needed: o Justifying the Exterior Angle of a Triangle Theorem 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.